Higher regularity for minimizers of very degenerate integral functionals

Mons L (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Journal of Mathematical Analysis and Applications Elsevier

Book Volume: 518

Article Number: 126717

Journal Issue: 2

DOI: 10.1016/j.jmaa.2022.126717

Abstract

In this article, we consider minimizers of integral functionals of the type [Formula presented] with a bounded domain Ω⊂Rⁿ(n≥2), a growth exponent p≥2 and Lipschitz continuous coefficients a:Ω→R. We consider the vectorial setting, i.e. u:Ω→R^N with N≥1. We will prove that H(Du) is continuous for any continuous function H:R^Nn→R vanishing on {ξ∈R^Nn:|ξ|≤1}. This extends a recent result from [3] to the case of integrands that explicitly depend on the x-variable.

Authors with CRIS profile

Léon Mons Lehrstuhl für Partial Differential Equations

How to cite

APA:

Mons, L. (2023). Higher regularity for minimizers of very degenerate integral functionals. Journal of Mathematical Analysis and Applications, 518(2). https://doi.org/10.1016/j.jmaa.2022.126717

MLA:

Mons, Léon. "Higher regularity for minimizers of very degenerate integral functionals." Journal of Mathematical Analysis and Applications 518.2 (2023).

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