FREE BOUNDARY VALUE PROBLEMS FOR QUASI LINEAR ELLIPTIC EQUATIONS

Suncica Canic, University of Houston Barbara Lee Keyfitz, University of Houston Eun Heui Kim, California State University at Long Beach

AMS classification: 35J25, 35J70,35L65

Keywords: Free boundary, quasilinear degenerate elliptic.

Abstract. We discuss existence results for a class of free boundary value problems for quasilinear elliptic equations. In the study of self-similar solutions for two-dimensional conservation laws, the governing equations change type in some regions. There, many interesting elliptic boundary value problems can be formulated; such as quasilinear degenerate elliptic problems with mixed boundary condition, nonlinear free boundary problems, degenerate oblique boundary problems and so on. These problems arise in many different combinations. In this talk we formulate a class of free boundary value problems for quasilinear degenerate elliptic equations arising changeof-type systems in conservation laws and outline the solution.