On boundary values of solutions of a quasi-linear partial differential equation of elliptic type
Jan H. Chabrowski · Rocky Mountain Journal of Mathematics · 1986
Introduction.In this article we study traces of generalized solutions of quasi-linear elliptic equations.We obtain a sufficient condition for a solution in Wfc*{Q) to have an L 2 -trace on the boundary.The results are then applied to establish an existence theorem for the Dirichlet problem.The arguments which we giwt here are based partially on the references [2] and [4].The outline of this paper is as follows.§1 contains preliminary work.§2 deals with the problem of traces for solutions in Wfe?(Q).The main result here is Theorem 1, which justifies the approach to the Dirichlet problem adopted in §4.In §3 we derive an energy estimate for solutions of the Dirichlet problem with L 2 -boundary data.