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arXiv · 1810.04976

A stationary heat conduction problem

Piotr Rybka·Anna Zatorska-Goldstein
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Abstract

We study a basic linear elliptic equation on a lower dimensional rectifiable set $S$ in $\mathbb{R}^N$ with the Neumann boundary data. Set $S$ is a support of a finite Borel measure $\mu$. 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 $\mu$. We establish existence and uniqueness of weak solutions provided that an appropriate source term is given.

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Piotr Rybka, Anna Zatorska-Goldstein. 2018-10-11. A stationary heat conduction problem. https://arxiv.org/abs/1810.04976

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