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Giovanni Leoni |
Selected Publications
Books
1) Modern Methods in the Calculus of Variations: L^p Spaces, (with I. Fonseca), Springer Monographs in Mathematics, Springer, 2007
2) Modern Methods in the Calculus of Variations: Sobolev Spaces, (with I. Fonseca), in preparation, to appear in Springer-Verlag
Papers
Energies for incoherent interfaces: an analytical approach, (with P. Cermelli and M. Gurtin), Interfaces and Free Boundaries 1 (1999) 81--105;
Interfacial energies for incoherent inclusions, (with P. Cermelli), Archive Rational Mech. Anal. 159 (2001) 335--361;
A Gamma-convergence result for the two-gradient theory of phase transitions, (with S. Conti and I. Fonseca), Comm. Pure Appl. Math. 55 (2002) 857--936;
A global method for relaxation in W^{1,p} and in SBV_{p}, (with G. Bouchitte', I. Fonseca and L. Mascharenhas), Arch. Ration. Mech. Anal. 165 (2002) 187-242;
Higher Order Quasiconvexity Reduces to Quasiconvexity (with G. Dal Maso, I. Fonseca and M. Morini), Archive Rational Mech. Anal. 171 (2004), no. 1, 55--81;
A-quasiconvexity: the gap problem, (with I. Fonseca and S. Mueller), Ann. Inst. H. Poincar Anal. Non Linaire 21 (2004), no. 2, 209-236;
"On optimal regularity of free boundary problems and a conjecture of De Giorgi (with H. Koch and M. Morini), Comm. Pure Appl. Math. 58 (2005), no. 8, 1051--1076;
Weak continuity and lower semicontinuity results for determinants (with I. Fonseca and J. Maly), Arch. Ration. Mech. Anal. 178 (2005), no. 3, 411--448;
Renormalized Energy and Forces on Dislocations (with P. Cermelli), SIAM J. Math. Anal. 37 (2005), no. 4, 1131--1160;
Necessary and sufficient conditions for the chain rule in $W_{loc}^{1,1}(R^N;R^d)$ and $BV_{loc}(R^N;R^d)$ (with M. Morini) to appear in the Journal of the European Mathematic Society (JEMS).;
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