Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients
arxiv(2017)
Abstract
We obtain new partial Hölder 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 𝒜-harmonic approximation, we are able to allow for both VMO-discontinuities in the coefficients, and the minimal log-Hölder regularity assumption on the exponent function. In doing so, we recover a local version of the quantisation phenomenon characteristic continuous coefficient case.
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