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

François Générau; Edouard Oudet

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

Optimization and Control 2018-02-12 v2 Analysis of PDEs

Authors: François Générau , Edouard Oudet

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.

Keywords

nonlocal isoperimetric problem volume-constrained minimization riesz potential external potential variational problem numerical method large volume minimizers

Cite

@article{arxiv.1707.06028,
  title  = {Large volume minimizers of a non local isoperimetric problem: theoretical and numerical approaches},
  author = {François Générau and Edouard Oudet},
  journal= {arXiv preprint arXiv:1707.06028},
  year   = {2018}
}

Comments

This improved version contains some minor modifications, new references, and one extra numerical experiment

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

Abstract

Keywords

Cite

Comments

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