## $$L^p$$ 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

### Keywords:

$$L^p$$ estimates; elliptic system; BMO space; Reifenberg domain
Full Text: