Geodesic
Partial Regularity for Minimizers of Degenerate Polyconvex Energies
Journal of convex analysis, Tome 8 (2001) no. 1, pp. 1-38 Cet article a éte moissonné depuis la source Heldermann Verlag

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We prove partial regularity of minimizers for a class of polyconvex integral functionals $$ \int_\Omega f (Du, \text{Ad}\, Du, \text{det}\, Du)\, dx, $$ where $f$ is degenerate convex. Our class includes the model case $$ \int_\Omega (|Du|^p + |\text{Ad}\, Du|^p + |\text{det}\, Du|^p)\, dx. $$ The method of proof involves a blow-up technique combined with a suitable asymptotic analysis of the degeneration nature of the first term $\int_\Omega |Du|^p\, dx$.
Classification : 49N60, 49N99, 35J20
Mots-clés : Polyconvexity, regularity, elliptic systems 
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     author = {L. Esposito and G. Mingione},
     title = {Partial {Regularity} for {Minimizers} of {Degenerate} {Polyconvex} {Energies}},
     journal = {Journal of convex analysis},
     pages = {1--38},
     year = {2001},
     volume = {8},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a0/}
}
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L. Esposito; G. Mingione. Partial Regularity for Minimizers of Degenerate Polyconvex Energies. Journal of convex analysis, Tome 8 (2001) no. 1, pp. 1-38. http://geodesic.mathdoc.fr/item/JCA_2001_8_1_JCA_2001_8_1_a0/