We show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theory. In particular, in the setting of functionals with (p, q)growth - according to the terminology of Marcellini [52] - we derive optimal local regularity criteria under minimal assumptions on the data. (c) 2022 Elsevier Masson SAS. All rights reserved.
Quasiconvexity and partial regularity via nonlinear potentials / De Filippis, C. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 163:(2022), pp. 11-82. [10.1016/j.matpur.2022.05.001]
Quasiconvexity and partial regularity via nonlinear potentials
De Filippis, C
2022-01-01
Abstract
We show how to infer sharp partial regularity results for relaxed minimizers of degenerate, nonuniformly elliptic quasiconvex functionals, using tools from Nonlinear Potential Theory. In particular, in the setting of functionals with (p, q)growth - according to the terminology of Marcellini [52] - we derive optimal local regularity criteria under minimal assumptions on the data. (c) 2022 Elsevier Masson SAS. All rights reserved.File in questo prodotto:
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