Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients

arXiv1711.01389MaRDI QIDQ6293475

Chris van der Heide

Publication date: 3 November 2017

Abstract: We obtain new partial H"older continuity results for solutions to divergence form elliptic systems with discontinuous coefficients, obeying $p(x)$-type nonstandard growth conditions. By an application of the method of $mathcalA$-harmonic approximation, we are able to allow for both VMO-discontinuities in the coefficients, and the minimal $log$-H"older regularity assumption on the exponent function. In doing so, we recover a local version of the quantisation phenomenon characteristic continuous coefficient case.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order elliptic systems (35J47)

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