Partial regularity for minima of higher order functionals with p(x) growth

2006/10/04 by Jens Habermann, Habermann, Jens
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0610145

29 pages

arxiv created 2006/10/04 · arxiv updated 2009/12/01

Abstract

For higher order integral functionals with p(x) growth with respect to the highest order derivative D^m u, we prove that D^m u is Hölder continuous on an open subset Ω₀ ⊂ Ω of full Lebesgue- measure, provided that the exponent function p:Ω→ (1,∞) itself is Hölder continuous.

Related

• Regularity results for Hölder minimizers to functionals with non-standard growth
• Hölder continuity and differentiability on subsequences
• A lower semicontinuity result for some integral functionals in the space SBD
• A necessary condition on a singular kernel for the continuity of an integral operator in Hölder spaces
• Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth