On Pompeiu's-Schiffer's Conjectures from Shape Optimization

Diaraf Seck

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arXiv · 2405.11700

On Pompeiu's-Schiffer's Conjectures from Shape Optimization

Diaraf Seck

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Abstract

Our aim is to do a come back on Schiffer's and Pompeiu's conjectures with shape optimization tools, maximum principles and Serrin's symmetry method. We propose a way to get affirmative answers in some cases. We propose also sufficient conditions thanks to Riemannian approach of infinite dimension that could be useful for numerical simulations of the shape of domains related to these conjectures.

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Diaraf Seck. 2024-05-19. On Pompeiu's-Schiffer's Conjectures from Shape Optimization. https://arxiv.org/abs/2405.11700

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