Pré-Publication, Document De Travail Année : 2024

A concentration-compactness principle for perturbed isoperimetric problems with general assumptions

Résumé

Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely" distant from each other. In this article and under mild assumptions we establish existence and density estimates of generalized minimizers of perturbed isoperimetric problems. Our hypotheses encapsulate a wide class of functionals including the classical, anisotropic and fractional perimeter. The perturbation term may for instance take the form of a potential, a translation invariant kernel or a nonlocal term involving the Wasserstein distance.

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hal-04619882 , version 1 (21-06-2024)

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Jules Candau-Tilh. A concentration-compactness principle for perturbed isoperimetric problems with general assumptions. 2024. ⟨hal-04619882⟩
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