Asymptotic behavior of nonlinear Dirichlet problems in perforated domains - Gianni Dal Maso; Igor V. Skrypnik (Ann. Mat. Pura Appl. (4) 174 (1998), 13--72, 1998)

Branching points for a class of variational operators - Antonio Ambrosetti (J. Anal. Math. 76 (1998) 321-335, 1998)

On the Dirichlet problem for vectorial Hamilton-Jacobi equations - Sandro Zagatti (SIAM J. Math. Anal. 29 (1998) 1481-1491, 1998)
We give sufficient conditions for the existence of solutions to the Hamilton--Jacobi equations with Dirichlet boundary condition: $$ \\\\cases{ g(x,{\\\\hbox{\\\\rm det}}Du(x))=0, \\\\ & for a.e. $x\\\\in\\\\Omega,$\\\\cr u(x)=\\\\varphi(x), & for $x\\\\in\\\\partial\\\\Omega,$} $$ obtaining, in addition, an application to the theory of existence of minimizers for a class of nonconvex variational problems.

Error bounds for a deterministic version of the Glimm scheme - Andrea Marson; Alberto Bressan (Arch. Rational Mech. Anal. 142 (1998), no. 2, 155-176, 1998)
Consider the hyperbolic system of conservation laws $u_t F(u)_x=0. Let $u$ be the unique viscosity solution with initial condition $u(0,x)=\\\\bar u(x)$ and let $u^\\\\varepsilon$ be an approximate solution constructed by the Glimm scheme, corresponding to the mesh sizes $\\\\Delta x,\\\\Delta t=O(\\\\Delta x). With a suitable choise of the sampling sequence, we prove the estimate $$ \\\\left\\\\Vert u^\\\\varepsilon(t,\\\\cdot)-u(t,\\\\cdot) \\\\right\\\\Vert_1=o(1)\\\\cdot\\\\sqrt{\\\\Delta x}\\\\vert\\\\ln\\\\Delta x\\\\vert. $$

A generic classification of time-optimal planar stabilizing feedbacks - Alberto Bressan; Benedetto Piccoli (SIAM J. Control Optim. 36 (1998) 12-32, 1998)
Consider the problem of stabilization at the origin in minimum time for a planar control system affine with respect to the control. For a family of generic vector fields, a topological equivalence relation on the corresponding time-optimal feedback synthesis was introduced in a previous paper [Dynamics of Continuous, Discrete and Impulsive Systems, 3 (1997), pp. 335--371]. The set of equivalence classes can be put in a one-to-one correspondence with a discrete family of graphs. This provides a classification of the global structure of generic time-optimal stabilizing feedbacks in the plane, analogous to the classification of smooth dynamical systems developed by Peixoto.

Geometric control approach to synthesis theory - Ugo Boscain; Benedetto Piccoli (Rend. Sem. Mat. Univ. Politec. Torino 56 (1998), no. 4, 53-68 (2001), 1998)

Infinite time regular synthesis - Benedetto Piccoli (ESAIM: COCV 3 (1998) 381-405, 1998)
In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach the target in finite time with a finite number of switchings. In the case of this paper the situation is even more complicate, since we admit both trajectories with finite and infinite time. We use weak differentiability assumptions on the synthesis and weak continuity assumptions on the associated value function.

Limits of variational problems for Dirichlet forms in varying domains - Gianni Dal Maso; Virginia De Cicco; Lino Notarantonio; Nicoletta A. Tchou (Journal des Mathematiques Pures et Appliquees. Volume 77, Issue 1, January 1998, Pages 89-116, 1998)

Special functions with bounded variation and with weakly differentiable traces on the jump set - Luigi Ambrosio; Andrea Braides; Adriana Garroni (NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243, 1998)

Uniqueness for discontinuous ODE and conservation laws - Alberto Bressan; Wen Shen (Nonlinear Analysis 34 (1998) 637-652, 1998)
Consider a scalar O.D.E. of the form $\\\\dot x=f(t,x),$ where $f$ is possibly discontinuous w.r.t. both variables $t,x$. Under suitable assumptions, we prove that the corresponding Cauchy problem admits a unique solution, which depends H\\\\\\\"older continuously on the initial data.\\nOur result applies in particular to the case where $f$ can be written in the form $f(t,x)\\\\doteq g\\\\big( u(t,x)\\\\big)$, for some function $g$ and some solution $u$ of a scalar conservation law, say $u_t+F(u)_x=0$. In turn, this yields the uniqueness and continuous dependence of solutions to a class of $2\\\\times 2$ strictly hyperbolic systems, with initial data in $\\\\L^\\\\infty$.

Capacity theory for monotone operators - Gianni Dal Maso; Igor V. Skrypnik (Potential Anal. 7 (1997), no. 4, 765-803, 1997)
If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1< p <+\\\\infty$, with $a(x,0)=0$ for a.e. $x\\\\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\\\\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$.

Comportamento asintotico delle soluzioni di problemi di Dirichlet - Gianni Dal Maso (Bollettino della Unione Matematica Italiana A. Volume 7, Issue SUPPL. 11 part 2, June 1997, Pages 253-277, 1997)

On Existence and Continuous Dependence for Systems of Conservation Laws - Paolo Baiti (SISSA, 1997)
Keywords: Conservation laws

Homogeneous tangent vectors and high order necessary conditions for optimal controls - Fabio Ancona (J. Dynam. Control Systems 3 (1997), no. 2, 205--240, 1997)

The semigroup generated by a temple class system with large data - Paolo Baiti; Alberto Bressan (Differential Integral Equations 10 (1997), no. 3, 401-418, 1997)
We consider the Cauchy problem $$u_t + [F(u)]_x=0, u(0,x)=\\\\bar u(x) (*)$$ for a nonlinear $n\\\\times n$ system of conservation laws with coinciding shock and rarefaction curves. Assuming the existence of a coordinates system made of Riemann invariants, we prove the existence of a weak solution of (*) that depends in a lipschitz continuous way on the initial data, in the class of functions with arbitrarily large but bounded total variation.

Shift-differentiability of the flow generated by a conservation law - Alberto Bressan; Graziano Guerra (Discrete Contin. Dynam. Systems 3 (1997), no. 1, 35--58., 1997)
The paper introduces a notion of \\\"shift-differentials\\\" for maps with values in the space BV. These differentials describe first order variations of a given functin $u$, obtained by horizontal shifts of the points of its graph. The flow generated by a scalar conservation law is proved to be generically shift-differentiable, according to the new definition.

Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains - Rodica Toader (SISSA, 1997)
Keywords: Dirichlet problems

Some properties of reachable solutions of nonlinear elliptic equations with measure data - Gianni Dal Maso; Annalisa Malusa (Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396, 1997)

Structural stability for time-optimal planar sytheses - Alberto Bressan; Benedetto Piccoli (Dynam. Contin. Discrete Impuls. Systems 3 (1997), no. 3, 335--371, 1997)

Viscosity solutions and uniquenessfor systems of inhomogeneous balance laws - Graziano Crasta; Benedetto Piccoli (Discrete Contin. Dynam. Systems 3 (1997), no. 4, 477--5, 1997)

A capacity method for the study of Dirichlet problems for elliptic systems in varying domains - Gianni Dal Maso; Rodica Toader (Rend. Sem. Mat. Univ. Padova 96 (1996), 257--277, 1996)

The semigroup approach to systems of conservation laws - Alberto Bressan (Mat. Contemp. 10 (1996) 21-74, 1996)

Solving Honig generic problem about Volterra integral equations - Giovanni Vidossich (Bull. Polish Acad. Sci. Math. 44 (1996), no. 4, 495--498, 1996)

Capacity and Dirichlet problems in varying domains - Gianni Dal Maso (SISSA Library, 1995)

An existence result in a problem of the vectorial case of the calculus of variations - Arrigo Cellina; Sandro Zagatti (SIAM, 1995)
SIAM J. Control Optim. 33 (1995) 960-970

Some control problems for the pendulum - Benedetto Piccoli (Proceedings of the 34th IEEE Conference on Decision and Control 4 (1995) 3313-3318, 1995)
The aim of this paper is to illustrate some geometric techniques for the study of nonlinear systems. The pendulum on one hand is good for its simplicity, on the other it presents many of the difficulties one can encounter treating nonlinear systems.

Special functions of bounded deformation - Giovanni Bellettini; Alessandra Coscia; Gianni Dal Maso (SISSA Library, 1995)

Unique solutions of 2x2 conservation laws with large data - Alberto Bressan; Rinaldo M. Colombo (Indiana Univ. Math. J. 44 (1995), no. 3, 677-725, 1995)
For a 2x2 hyperbolic system of conservation laws, we first consider a Riemann problem with arbitrarily large data. A stability assumption is introduced, which yields the existence of a Lipschitz semigroup of solutions, defined on a domain containing all suitably small BV perturbations of the Riemann data. We then establish a uniqueness result for large BV solutions, valid within the same class of functions where a local existence theorem can be proved.

Asymptotic Behaviour of Dirichlet Problems in Perforated Domains - Adriana Garroni (SISSA, 1994)
Keywords: Dirichlet problems

Limits of Dirichlet problems in perforated domains: a new formulation - Gianni Dal Maso; Rodica Toader (Rend. Istit. Mat. Univ. Trieste 26 (1994) 339-360, 1994)

A version of Olech\\\'s lemma in a problem of the calculus of variations - Arrigo Cellina; Sandro Zagatti (SIAM J. Control Optim. 32 (1994) 1114-1127, 1994)
This paper studies the solutions of the minimum problem for a functional of the gradient under linear boundary conditions. A necessary and sufficient condition, based on the facial structure of the epigraph of the integrand, is provided for the continuous dependence of the solutions on boundary data.

Some Problems in the Calculus of the Variations - Sandro Zagatti (SISSA, 1992)
Keywords: Calculus of variations

A variational method in image segmentation: existence and approximation result - Gianni Dal Maso; Jean-Michel Morel; Sergio Solimini (Acta Math. 168 (1992), no.1-2, p. 89-151, 1992)

A class of absolute retracts of dwarf spheroidal galaxies - Alberto Bressan; Arrigo Cellina; Andrzej Fryszkowski (Proc.Amer.Math.Soc. 112 (1991), no.2, 413, 1991)

Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions - Giuseppe Buttazzo; Gianni Dal Maso (Appl.Math.Optim. 23 (1991), no.1, p. 17-49., 1991)

On systems of ordinary differential equations with measures as controls - Gianni Dal Maso; Franco Rampazzo (Differential Integral Equations 4 (1991), no.4, p.739-765., 1991)

Correctors for the homogeneization of monotone operators - Gianni Dal Maso; Anneliese Defranceschi (Differential Integral Equations 3 (1990), no.6, p.1151-1166., 1990)

Existence and continuous dependence for discontinuous O.D.E.s - Alberto Bressan; Giovanni Colombo (Boll. Un. Mat. Ital. B (7) 4 (1990), no. 2, 295--311, 1990)

Existence of solutions for a class of non-convex differential inclusions - Fabio Ancona; Giovanni Colombo (Rend.Sem.Mat.Univ. Padova, 83 (1990), 71-76, 1990)

G-convergence of monotone operators - Valeria Chiadò Piat; Gianni Dal Maso; Anneliese Defranceschi (Ann. Inst. H. Poincare\\\' Anal. Non Linére 7 (1990), no. 3, 123-160, 1990)

A general chain rule for distributional derivatives - Luigi Ambrosio; Gianni Dal Maso (Proc. Amer. Math. Soc. 108 (1990), no. 3, 691-702, 1990)

A general existence theorem for boundary value problems for ordinary differential equations - Giovanni Vidossich (Nonlinear Anal. 15 (1990), no. 10, 897--914, 1990)

Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions - Giuseppe Buttazzo; Gianni Dal Maso (Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535., 1990)

An approach to the thin obstacle problem for variational functionals depending on vector - Gianni Dal Maso; Roberta Musina (Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743., 1989)

On the continuous dependence of solutions of boundary value problems for ordinary differential equations (Revised version) - Giovanni Vidossich (J. Differential Equations 82 (1989), no. 1, 1-14, 1989)

On the continuous dependence of solutions of boundary value problems for ordinary differential equations - Giovanni Vidossich (J. Differential Equations 82 (1989), no. 1, 1--14, 1989)

Convergence of unilateral problems for monotone operators - Gianni Dal Maso; Anneliese Defranceschi (J. Analyse Math. 53 (1989), 269--289, 1989)

Hyperbolic equations as ordinary differential equations in Banach spaces - Giovanni Vidossich (SISSA Library, 1989)

Limits of obstacle problems for the area functional. - Gianni Dal Maso; G. Carere; Antonio Leaci; Eduardo Pascali (Partial differential equations and the calculus of variations : essays in honor of Ennio De Giorgi. - Boston : Birkhauser, 1989. - p. 285-309, 1989)

A pointwise regularity theory for the two-obstacle problem - Gianni Dal Maso; Umberto Mosco; Maria Agostina Vivaldi (Acta Math. 163 (1989), no. 1-2, 57-107, 1989)

On the solvability of boundary value problems for higher order ordinary differential equations (Revised version) - Giovanni Vidossich (Nonlinear Anal. 13 (1989), no. 10, 1171-1179, 1989)

On the solvability of boundary value problems for higher order ordinary differential equations - Giovanni Vidossich (Nonlinear Anal. 13 (1989), no. 10, 1171-179, 1989)

Surfaces of minimal area enclosing a given body in R\\\\sp 3. - Giovanni Mancini; Roberta Musina (Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), no. 3, 331--354 (1990)., 1989)

Upper semicontinuous differential inclusions without convexity - Alberto Bressan; Arrigo Cellina; Giovanni Colombo (Proc. Amer. Math. Soc. 106 (1989), no. 3, 771-775, 1989)

On differential systems with vector-valued impulsive controls. - Alberto Bressan; Franco Rampazzo (Boll. Un. Mat. Ital. B (7) 2 (1988), no. 3, 641-656, 1988)

Generalized Baire category and differential inclusions in Banach spaces. - Alberto Bressan; Giovanni Colombo (J. Differential Equations 76 (1988), no. 1, 135-158., 1988)

Holes and obstacles - Roberta Musina; Giovanni Mancini (Ann. Inst. H. Poincare Anal. Non Lineaire 5 (1988), no. 4, 323-345, 1988)

H-surfaces with obstacles. (Italian) - Roberta Musina (Ann. Univ. Ferrara Sez. VII (N.S.) 34 (1988), 1-14, 1988)

A Kellogg property for µ-capacities - Gianni Dal Maso; Anneliese Defranceschi (Boll. Un. Mat. Ital. A (7) 2, 1988, no. 1, 127-135, 1988)

Limits of nonlinear Dirichlet problems in varying domains. - Gianni Dal Maso; Anneliese Defranceschi (Manuscripta Math. 61 (1988), no. 3, 251-278., 1988)
We study the general form of the limit, in the sense of gamma-convergence, of a sequence of nonlinear variational problems in varying domains with Dirichlet boudary conditions. The asymptotic problem is characterized in terms of the limit of suitable nonlinear capacities associated to the domains.

Some properties of a class of nonlinear variational $m$-capacities - Gianni Dal Maso; Anneliese Defranceschi (J.Funct.Anal. 79, 1988, no. 2, 476-492, 1988)

Variational inequalities for the biharmonic operator with variable obstacles. - Gianni Dal Maso; Gabriella Paderni (Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989), 1988)

Variational Problems with Obstructions - Roberta Musina (SISSA, 1988)

Integral representation of some convex local functionals. - Gianni Dal Maso; Gabriella Paderni (Ricerche Mat. 36 (1987), no. 2, 197-214, 1987)

Limits of nonlinear Dirichlet problems in varying domains. (Italian) - Gianni Dal Maso; Anneliese Defranceschi (Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 81, 1987, no. 2, 111-118, 1987)

Solutions with minimal period for Hamiltonian systems in a potential well. - Antonio Ambrosetti; Vittorio Coti Zelati (Ann. Inst. H. Poincare Anal. Non Lineaire 4 (1987), no. 3, 275-296, 1987)

Symmetry breaking in Hamiltonian systems - Antonio Ambrosetti; Vittorio Coti Zelati; Ivar Ekeland (J. Differential Equations 67 (1987), no. 2, 165-184, 1987)

Convergence of unilateral convex sets. Optimization and related fields (Erice, 1984) - Gianni Dal Maso (Berlin : Springer-Verlag, 1986, Lecture notes in mathematics, v.1190, p. 181-190, 1986)

Dirichlet problems for demicoercive functionals - Gabriele Anzellotti; Giuseppe Buttazzo; Gianni Dal Maso (Nonlinear anal. 10(1986), no.6, 603-613, 1986)

Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets - Gianni Dal Maso (J. Funct. Anal. 62 (1985), no. 2, 119--159, 1985)

Some singular perturbation problems in the calculus of variations. - Gianni Dal Maso (Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985, 1985)

The two-point boundary value problem from the Cauchy problem - Giovanni Vidossich (J. Differential Equations 60 (1985), no. 1, 1--20, 1985)

Weak convergence of measures on spaces of semicontinuous functions. - Gianni Dal Maso; Ennio De Giorgi; Luciano Modica (Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106, 1985)

On the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations - Giovanni Vidossich (SISSA Library, 1983)

Towards a theory for periodic solutions to first order ordinary differential equations. - Giovanni Vidossich (SISSA Library, 1983)

A criterion for he existence of maximal solutions of strongly nonlinear elliptic problems - Giovanni Vidossich (SISSA Library, 1982)

Differential equations with multiple solutions and nonlinear functional analysis - Antonio Ambrosetti (Equadiff 82 (Wurzburg, 1982), 10--37, Lecture Notes in Math., 1017, Springer, Berlin, 1983, 1982)

On the obstacle problem for strongly nonlinear elliptic equations - Giovanni Vidossich (SISSA Library, 1982)

Three uniqueness theorems for strongly non-linear elliptic problems - Giovanni Vidossich (SISSA Library, 1982)

Recent advances in the study of the existence of periodic orbits of Hamiltonian systems - Antonio Ambrosetti (Advances in Hamiltonian systems (Rome, 1981), 1--22, Ann. CEREMADE, Birkhauser Boston, Boston, MA, 1983., 1981)

Uniqueness and multiplicity of periodic solutions to first order ordinary differential equations - Giovanni Vidossich (Not Found)