Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth. Issue 5 (October 2022)

• Record Type: Journal Article
• Authors: Goodrich, Christopher; Scilla, Giovanni; Stroffolini, Bianca
• Is Part Of: Proceedings. Volume 152:Issue 5(2022)
• Page Start: 1191
• Page End: 1232
• Publication Date: 2022-10
• Subjects: partial regularity -- Morrey estimates -- general growth -- VMO condition; 35J70 -- 35B65 -- 46E30; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2021.53
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x, {\bf u}, D{\bf u})\, \textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to the $x$ -variable and is continuous with respect to ${\bf u}$ . The growth condition with respect to the gradient variable is assumed a general one.