Regularity of local minimizers of the interaction energy via obstacle problems.
Seminar Room 2, Newton Institute Gatehouse
AbstractLocal minimizers of the interaction energy present a very rich structure. We show that if the repulsion at the origin is strong enough but integrable, then the local minimizers are in fact regular, at least bounded probability densities, and they satisfy an implicit obstacle problem. This is the key to establish also uniqueness of global minimizers upto translations in some particular case. This is a work in collaboration with M. Delgadino and A. Mellet.
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