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On the \(W^{1,q}\) estimate for weak solutions to a class of divergence elliptic equations. (English) Zbl 1136.35389

Summary: Local \(W^ {1,q}\) estimates for weak solutions for equations in the form \[ D_ i(a_ {ij}(x)| Du| ^ {p-2}D_ ju)=0 \] are obtained, where \(q>p\) is given. These estimates are very important in obtaining higher regularity for the weak solutions of elliptic equations.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35B45 A priori estimates in context of PDEs
35J60 Nonlinear elliptic equations
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