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arXiv · 1907.12523

A Uniqueness Theorem for Mean Value Sets for Elliptic Divergence Form Operators

Niles Armstrong·Ivan Blank
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Abstract

We give background which shows the connection between the mean value theorem and the obstacle problem, and then we prove that a set is a mean value set for an elliptic operator of the form $Lu := \partial_i (a^{ij}(x) \partial_j u(x))$ if and only if it arises as the noncontact set of an obstacle problem involving the Green's function of the operator.

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Niles Armstrong, Ivan Blank. 2019-07-29. A Uniqueness Theorem for Mean Value Sets for Elliptic Divergence Form Operators. https://arxiv.org/abs/1907.12523

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