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Volume 16, Issue 1
Two Dimensional Interface Problems for Elliptic Equations

Lung-an Ying

J. Part. Diff. Eq., 16 (2003), pp. 37-48.

Published online: 2003-02

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  • 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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COPYRIGHT: © Global Science Press

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@Article{JPDE-16-37, author = {Lung-an Ying}, title = {Two Dimensional Interface Problems for Elliptic Equations}, journal = {Journal of Partial Differential Equations}, year = {2003}, volume = {16}, number = {1}, pages = {37--48}, 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5404.html} }
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.
Lung-an Ying. (2003). Two Dimensional Interface Problems for Elliptic Equations. Journal of Partial Differential Equations. 16 (1). 37-48. doi:
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