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

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.

arXiv comment14 pages; Differential and Integral Equations, 2012

Cited by in corpus (2)

• Boundedness of Solutions to a Class of Coercive Systems with Morrey Data
• Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data