Differential and Integral Equations

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

Lubomira G. Softova

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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

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

First available in Project Euclid: 3 July 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J57: Boundary value problems for second-order elliptic systems 35K51: Initial-boundary value problems for second-order parabolic systems 35B40: Asymptotic behavior of solutions


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

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