Regularity of solutions to some degenerate double obstacle problems. (English) Zbl 0767.35029

Lieberman, Gary M.

Indiana Univ. Math. J. 40, No. 3, 1009-1028 (1991).

Summary: We study double obstacle problems for a class of elliptic operators modelled on the \(p\)-Laplacian operator: \(Qu=\text{div}(| Du|_{P-2} Du)\) for \(p>1\). When the obstacles are \(C^{1,\alpha}\) (with \(\alpha\) sufficiently small), so is the solution; this regularity is proved both locally and up to the boundary.

MSC:

35J85	Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35J70	Degenerate elliptic equations
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

regularity up to the boundary; \(p\)-Laplacian