Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches

François Générau; Edouard Oudet

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arXiv · 1707.06028

Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches

François Générau·Edouard Oudet

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Abstract

We consider the volume-constrained minimization of the sum of the perimeter and the Riesz potential. We add an external potential of the form $\|x\|^{\beta}$ that provides the existence of a minimizer for any volume constraint, and we study the geometry of big minimizers. Then we provide a numerical method to adress this variational problem.

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François Générau, Edouard Oudet. 2017-07-19. Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches. https://arxiv.org/abs/1707.06028

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