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

Byun, Sun-Sig; Chen, Hongbin; Kim, Mijoung; Wang, Lihe

Discrete Contin. Dyn. Syst. 18, No. 1, 121-134 (2007).

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