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Two Dimensional Interface Problems for Elliptic Equations |
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| Authors: | Lung-an Ying |
| 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, α}-norm of the solution, and the equation only. |
| Keywords: | Quasilinear elliptic equations interface problems weak solutions singular points |
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