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On the higher integrability for certain nonlinear problems. (English) Zbl 1224.35128

The local higher integrability for gradients of solutions to a large class of elliptic equations of the type \(\operatorname {div}A(x,\nabla u)=0\) is studied. By investigation of the deviation (in a suitable sense) of the operator \(A\) to be constant with respect to \(x\) the higher integrability is established.

MSC:

35J60 Nonlinear elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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