Quasiconvexity and partial regularity via nonlinear potentials

2021/05/02 by Cristiana De Filippis, De Filippis, Cristiana · 5 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2105.00503

openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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