TY - JOUR
T1 - Two Dimensional Interface Problems for Elliptic Equations
AU - Lung-an Ying
JO - Journal of Partial Differential Equations
VL - 1
SP - 37
EP - 48
PY - 2003
DA - 2003/02
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5404.html
KW - Quasilinear elliptic equations
KW - interface problems
KW - weak solutions
KW - singular points
AB -  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,α}-norm of the solution, and the equation only.