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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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