Regularity for minimizers of scalar integral functionals

2024/06/27 by Grimaldi, Antonio Giuseppe, Mascolo, Elvira, di Napoli, Antonia Passarelli · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.19174

Abstract

We prove the local Lipschitz regularity of the local minimizers of scalar integral functionals of the form F(v;Ω)= ∫_Ω f (x, Dv) dx under (p,q)-growth conditions. The main novelty is that, beside a suitable regularity assumption on the partial map x↦ f(x,ξ), we do not assume any special structure for the energy density as a function of the ξ-variable.

Cited by

• Regularity for minimizers of degenerate, non-autonomous, orthotropic integral functionals
• Local Lipschitz continuity for energy integrals under unified general growth of fast and slow type

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• Lipschitz regularity for degenerate elliptic integrals with p,q-growth