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arXiv · 1511.05934

A Free Boundary Problem Related to Thermal Insulation

Luis A. Caffarelli·Dennis Kriventsov
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Abstract

We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but rather a hypersurface along which a harmonic function satisfies a Robin condition. We show that minimal sets exist, satisfy uniform density estimates, and, under some geometric conditions, have "locally flat" boundaries.

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Luis A. Caffarelli, Dennis Kriventsov. 2016-05-31. A Free Boundary Problem Related to Thermal Insulation. https://arxiv.org/abs/1511.05934

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