Two Dimensional Interface Problems for Elliptic Equations

Abstract

" We study the structure of solutions to the interface problems for second order quasi-linear elliptic partial differential equations in two dimensional space. We prove that each weak solution can be decomposed into two parts near singular points, a finite sum of functions in the form of cr^α log^m rφ(θ) and a regular one w. The coefficients c and the C^{1,α} norm of w depend on the H¹-norm and the C^{o,\u000bα}-norm of the solution, and the equation only."