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Boundary higher integrability for the gradient of distributional solutions of nonlinear systems. (English) Zbl 0869.49020
Summary: We consider distributional solutions to the Dirichlet problem for nonlinear elliptic systems of the type \[ \begin{cases} \text{div }A(x,u,Du)= \text{div }f\quad\text{in }\Omega,\\ u- u_0\in W^{1,r}_0(\Omega),\end{cases} \] with \(r\) less than the natural exponent \(p\) which appears in the coercivity and growth assumptions for the operator \(A\). We prove that \(Du\in W^{1,p}(\Omega)\) if \(|r-p|\) is small enough.

MSC:
49N60 Regularity of solutions in optimal control
35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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