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\(L^p\) regularity theory for linear elliptic systems. (English) Zbl 1189.35350

Summary: We consider the conormal derivative problem for an elliptic system in divergence form with discontinuous coefficients in a more general geometric setting. We obtain the \(L^{p}\) , \(1 < p <\infty\), regularity of the maximum order derivatives of the weak solutions for such a problem.

MSC:

35R05 PDEs with low regular coefficients and/or low regular data
35R35 Free boundary problems for PDEs
35J15 Second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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