Lp-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients

TL;DR

This paper proves Lp-integrability of the gradient for solutions to certain quasilinear elliptic and parabolic systems with discontinuous coefficients, extending regularity results in complex domains.

Contribution

It establishes explicit Lp-integrability results for gradients of solutions to quasilinear systems with discontinuous coefficients in Reifenberg-flat domains.

Findings

Lp-integrability of solutions' gradients with p>2

Results apply to both elliptic and parabolic systems

Explicit dependence of p on data

Abstract

The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in Reifenberg-flat domain is considered. The lower order terms supposed to satisfy controlled growth conditions. It is obtained Lp-integrability with p>2 of the gradient of the solution where p depends explicitly on the data. An analogous result is obtained also for the Cauchy-Dirichlet problem for quasilinear parabolic systems.