## Differential and Integral Equations

### $L^p$-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients

Lubomira G. Softova

#### Abstract

The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in a Reifenberg-flat domain $\Omega$ is considered. The lower-order terms are supposed to satisfy controlled growth conditions in ${\mathbf u}$ and $D\mathbf {u}$. $L^p$-integrability with $p>2$ of $D{\mathbf u}$ is obtained, where $p$ depends explicitly on the data. An analogous result is obtained also for the Cauchy--Dirichlet problem for quasilinear parabolic systems.

#### Article information

Source
Differential Integral Equations, Volume 26, Number 9/10 (2013), 1091-1104.

Dates
First available in Project Euclid: 3 July 2013

Softova, Lubomira G. $L^p$-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients. Differential Integral Equations 26 (2013), no. 9/10, 1091--1104. https://projecteuclid.org/euclid.die/1372858563