Abstract
Interface problems for second order quasi–linear elliptic partial differential equations in a two–dimensional space are studied. We prove that each weak solution can be decomposed into two parts near singular points, one of which is a finite sum of functions of the form cr α logm rϕ (θ), where the coefficients c depend on the H 1–norm of the solution, the C 0,δ–norm of the solution, and the equation only; and the other one of which is a regular one, the norm of which is also estimated.
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This work is supported by the China State Major Key Project for Basic Researches and the Science Fund of the Ministry of Education of China.
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Ying, L.A. A Decomposition Theorem for the Solutions to the Interface Problems of Quasi–Linear Elliptic Equations. Acta Math Sinica 20, 859–868 (2004). https://doi.org/10.1007/s10114-004-0374-7
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DOI: https://doi.org/10.1007/s10114-004-0374-7