The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in a Reifenberg-flat domain Ω is considered. The lower-order terms are supposed to satisfy controlled growth conditions in u and Du. Lp-integrability with p>2 of Du is obtained, where p depends explicitly on the data. An analogous result is obtained also for the Cauchy--Dirichlet problem for quasilinear parabolic systems.
Lp-integrability of the gradient of solutions to quasilinear systems with discontinuous coefficients
SOFTOVA Lyoubomira
2013
Abstract
The Dirichlet problem for a class of quasilinear elliptic systems of equations with small-BMO coefficients in a Reifenberg-flat domain Ω is considered. The lower-order terms are supposed to satisfy controlled growth conditions in u and Du. Lp-integrability with p>2 of Du is obtained, where p depends explicitly on the data. An analogous result is obtained also for the Cauchy--Dirichlet problem for quasilinear parabolic systems.File in questo prodotto:
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