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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