Free boundary and mixed boundary value problems for quasilinear elliptic equations: tangential oblique derivative and degenerate Dirichlet boundary problems

摘要

We present Holder estimates and Holder gradient estimates for a class of free boundary problems with tangential oblique derivative boundary conditions provided the oblique vector beta does not vanish at any point on the boundary. We also establish the existence result for a general class of quasilinear degenerate problems of this type including nonlinear wave systems and the unsteady transonic small disturbance equation. (c) 2004 Elsevier Inc. All rights reserved.