A stationary heat conduction problem

2018/10/11 by Rybka, Piotr, Zatorska-Goldstein, Anna
#28A33 #35J20 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.04976

Abstract

We study a basic linear elliptic equation on a lower dimensional rectifiable set S in ℝ^N with the Neumann boundary data. Set S is a support of a finite Borel measure μ. We will use the measure theoretic tools to interpret the equation and the Neumann boundary condition. For this purpose we recall the Sobolev-type space dependent on the measure μ. We establish existence and uniqueness of weak solutions provided that an appropriate source term is given.

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