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September/October 2013 $L^p$-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients
Lubomira G. Softova
Differential Integral Equations 26(9/10): 1091-1104 (September/October 2013).

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.

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Lubomira G. Softova. "$L^p$-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients." Differential Integral Equations 26 (9/10) 1091 - 1104, September/October 2013.

Information

Published: September/October 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1299.35118
MathSciNet: MR3100078

Subjects:
Primary: 35B40, 35J57, 35K51

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.26 • No. 9/10 • September/October 2013
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