Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

TL;DR

This paper establishes boundary partial regularity for minimizers of certain quasiconvex functionals with general growth, under minimal regularity assumptions on the integrand.

Contribution

It proves boundary partial Hölder continuity for minimizers of quasiconvex functionals with general growth and VMO conditions, extending regularity theory to more general settings.

Findings

Boundary partial Hölder continuity of minimizers

Regularity results under VMO conditions

Extension to functionals with general growth

Abstract

We prove the partial H\"older continuity on boundary points for minimizers of quasiconvex non-degenerate functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\mathrm{d}x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$-variable, is continuous with respect to ${\bf u}$ and has a general growth with respect to the gradient variable.