Three Dimensional Interface Problems for Elliptic Equations

Abstract

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension. The set of singular points consists of some singular lines and some isolated singular points. It is proved that near a singular line or a singular point, each weak solution can be decomposed into two parts, a singular part and a regular part. The singular parts are some finite sum of particular solutions to some simpler equations, and the regular parts are bounded in some norms, which are slightly weaker than that in the Sobolev space H ².

Keywords

Elliptic equation / Interface problem / Singular line / Singular point / Particular solution / 35J40

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