Boundary higher integrability for the gradient of distributional solutions of nonlinear systems
Volume 123 / 1997
Studia Mathematica 123 (1997), 175-184
DOI: 10.4064/sm-123-2-175-184
Abstract
We consider distributional solutions to the Dirichlet problem for nonlinear elliptic systems of the type ${ div A(x, u, Du) = div f in Ω, u - u_0 ∈ W^{1,r}_0(Ω)$ with r less than the natural exponent p which appears in the coercivity and growth assumptions for the operator A. We prove that $Du ∈ W^{1,p}(Ω)$ if |r-p| is small enough.
