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^\u03b1 log^m r\u03c6(\u03b8) and a regular one w. The coefficients c and the C^{1,\u03b1} norm of w depend on the H\u00b9-norm and the C^{\u00ba,\u000b\u03b1}-norm of the solution, and the equation only."