%0 Journal Article %D 2013 %T Analytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces %A Gianni Dal Maso %A Irene Fonseca %A Giovanni Leoni %K singular nonlinear parabolic equations, Hilbert transform, thin films %X In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6]. %I Springer %G en %U http://hdl.handle.net/1963/7245 %1 7284 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2014-01-15T08:47:14Z No. of bitstreams: 1 DM-Fon-Leo.pdf: 409459 bytes, checksum: 07429e936667a481a2c093217e585e84 (MD5) %R 10.1007/s00205-014-0730-4 %0 Report %D 2013 %T Attainment results for nematic elastomers %A Virginia Agostiniani %A Gianni Dal Maso %A Antonio DeSimone %X We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. %I SISSA %G en %U http://hdl.handle.net/1963/7174 %1 7201 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-10-22T14:32:26Z No. of bitstreams: 1 Ago-DM-DeS-13-sissa.pdf: 394672 bytes, checksum: d02690a6c7f206310d28d253ce53d0d3 (MD5) %0 Journal Article %J Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %D 2004 %T Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains %A Gianni Dal Maso %A Francois Murat %X We consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains. %B Ann. Inst. H. Poincaré. Anal. Non Linéaire 21 (2004), (4), p. 445-486. %I SISSA Library %G en %U http://hdl.handle.net/1963/1611 %1 2507 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:17Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0205225.pdf: 404809 bytes, checksum: 472524cb28afed2e55fcf0a7c46e7598 (MD5)\\r\\n Previous issue date: 2002 %0 Journal Article %J Applied Math.Optim. 48 (2003), no.1, p.39-66 %D 2003 %T Autonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations %A Gianni Dal Maso %A Helene Frankowska %B Applied Math.Optim. 48 (2003), no.1, p.39-66 %I SISSA Library %G en %U http://hdl.handle.net/1963/1625 %1 2493 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T13:05:30Z (GMT). No. of bitstreams: 1\\r\\nmath.AP0207230.pdf: 302400 bytes, checksum: e660ec855386e1a29edd2e20f7abc796 (MD5)\\r\\n Previous issue date: 2002 %R 10.1007/s00245-003-0768-4 %0 Journal Article %J Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %D 1999 %T Asymptotic behaviour of nonlinear elliptic higher order equations in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Journal d\\\'Analyse Mathematique, Volume 79, 1999, Pages: 63-112 %@ 1618-1891 %G en %U http://hdl.handle.net/1963/6433 %1 6374 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:25:49Z\\nNo. of bitstreams: 0 %R 10.1007/BF01759365 %0 Journal Article %J Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %D 1998 %T Asymptotic behavior of nonlinear Dirichlet problems in perforated domains %A Gianni Dal Maso %A Igor V. Skrypnik %B Ann. Mat. Pura Appl. (4) 174 (1998), 13--72 %I SISSA Library %G en %U http://hdl.handle.net/1963/1064 %1 2738 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:42:20Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995 %0 Journal Article %J Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %D 1989 %T An approach to the thin obstacle problem for variational functionals depending on vector %A Gianni Dal Maso %A Roberta Musina %B Comm. Partial Differential Equations, 14 (1989), no.12, 1717-1743. %I SISSA Library %G en %U http://hdl.handle.net/1963/802 %1 2989 %2 Mathematics %3 Functional Analysis and Applications %$ Made available in DSpace on 2004-09-01T12:38:08Z (GMT). No. of bitstreams: 0\\r\\n Previous issue date: 1989