TY - RPRT
T1 - Stochastic homogenisation of free-discontinuity problems
Y1 - 2018
A1 - Filippo Cagnetti
A1 - Gianni Dal Maso
A1 - Lucia Scardia
A1 - Caterina Ida Zeppieri
AB - In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.
UR - http://preprints.sissa.it/handle/1963/35309
U1 - 35617
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
TY - JOUR
T1 - Second Order Asymptotic Development for the Anisotropic Cahn-Hilliard Functional
Y1 - 2014
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
KW - Gamma-convergence, Cahn-Hilliard functional, phase transitions
AB - The asymptotic behavior of an anisotropic Cahn-Hilliard functional with prescribed mass and Dirichlet boundary condition is studied when the parameter $\varepsilon$ that determines the width of the transition layers tends to zero. The double-well potential is assumed to be even and equal to $|s-1|^\beta$ near $s=1$, with $1<\beta<2$. The first order term in the asymptotic development by $\Gamma$-convergence is well-known, and is related to a suitable anisotropic perimeter of the interface. Here it is shown that, under these assumptions, the second order term is zero, which gives an estimate on the rate of convergence of the minimum values.
PB - SISSA
UR - http://hdl.handle.net/1963/7390
N1 - This article is composed if 33 pages and recorded in PDF format
U1 - 7439
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Singular perturbation models in phase transitions for second order materials
JF - Indiana Univ. Math. J. 60 (2011) 367-409
Y1 - 2011
A1 - Milena Chermisi
A1 - Gianni Dal Maso
A1 - Irene Fonseca
A1 - Giovanni Leoni
AB - A variational model proposed in the physics literature to describe the onset of pattern formation in two-component bilayer membranes and amphiphilic monolayers leads to the analysis of a Ginzburg-Landau type energy with a negative term depending on the first derivative of the phase function. Scaling arguments motivate the study of the family of second order singular perturbed energies Fe having a negative term depending on the first derivative of the phase function. Here, the asymptotic behavior of {Fe} is studied using G-convergence techniques. In particular, compactness results and an integral representation of the limit energy are obtained.
PB - Indiana University
UR - http://hdl.handle.net/1963/3858
U1 - 851
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - ABST
T1 - Solutions of Neumann problems in domains with cracks and applications to fracture mechanics
Y1 - 2005
A1 - Gianni Dal Maso
UR - http://hdl.handle.net/1963/1684
U1 - 79
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A stability result for nonlinear Neumann problems under boundary variations
JF - J.Math. Pures Appl. (9) 82 (2003) no.5 , 503
Y1 - 2003
A1 - Gianni Dal Maso
A1 - Francois Ebobisse
A1 - Marcello Ponsiglione
AB - In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1618
U1 - 2500
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some properties of the solutions of obstacle problems with measure data
JF - Ricerche Matematiche., Supplemento dedicato a Ennio De Giorgi, vol. 48 (1999), page : 99-116
Y1 - 1999
A1 - Paolo Dall'Aglio
A1 - Gianni Dal Maso
UR - http://hdl.handle.net/1963/6432
U1 - 6372
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Some properties of reachable solutions of nonlinear elliptic equations with measure data
JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Sér. 4, 25 no. 1-2 (1997), p. 375-396
Y1 - 1997
A1 - Gianni Dal Maso
A1 - Annalisa Malusa
PB - SISSA
UR - http://hdl.handle.net/1963/6434
U1 - 6375
U2 - Mathematics
U4 - 1
U5 - MAT/05 ANALISI MATEMATICA
ER -
TY - JOUR
T1 - Special functions of bounded deformation
Y1 - 1995
A1 - Giovanni Bellettini
A1 - Alessandra Coscia
A1 - Gianni Dal Maso
PB - SISSA Library
UR - http://hdl.handle.net/1963/978
U1 - 3476
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Shape optimization for Dirichlet problems: relaxed formulations and optimally conditions
JF - Appl.Math.Optim. 23 (1991), no.1, p. 17-49.
Y1 - 1991
A1 - Giuseppe Buttazzo
A1 - Gianni Dal Maso
PB - SISSA Library
UR - http://hdl.handle.net/1963/880
U1 - 2911
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - On systems of ordinary differential equations with measures as controls
JF - Differential Integral Equations 4 (1991), no.4, p.739-765.
Y1 - 1991
A1 - Gianni Dal Maso
A1 - Franco Rampazzo
PB - SISSA Library
UR - http://hdl.handle.net/1963/840
U1 - 2951
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Shape optimization for Dirichlet problems: relaxed solutions and optimality conditions
JF - Bull. Amer. Math. Soc. (N.S.) , 23 (1990), no.2, 531-535.
Y1 - 1990
A1 - Giuseppe Buttazzo
A1 - Gianni Dal Maso
PB - SISSA Library
UR - http://hdl.handle.net/1963/809
U1 - 2982
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some properties of a class of nonlinear variational $m$-capacities
JF - J.Funct.Anal. 79, 1988, no. 2, 476-492
Y1 - 1988
A1 - Gianni Dal Maso
A1 - Anneliese Defranceschi
PB - SISSA Library
UR - http://hdl.handle.net/1963/485
U1 - 3419
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets
JF - J. Funct. Anal. 62 (1985), no. 2, 119--159
Y1 - 1985
A1 - Gianni Dal Maso
PB - SISSA Library
UR - http://hdl.handle.net/1963/318
U1 - 3649
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Some singular perturbation problems in the calculus of variations.
JF - Ennio De Giorgi Colloquium, p. 41-49, Research Notes in Mathematics, v.125, London : Pitman, 1985
Y1 - 1985
A1 - Gianni Dal Maso
PB - SISSA Library
UR - http://hdl.handle.net/1963/297
U1 - 3670
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -