A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects

Aleks Jevnikar; Wen Yang

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arXiv · 1605.08560

A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects

Aleks Jevnikar·Wen Yang

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Abstract

We are concerned with an elliptic problem which describes a mean field equation of the equilibrium turbulence of vortices with variable intensities. In the first part of the paper we describe the blow-up phenomenon and highlight the differences from the standard mean field equation. In the second part we discuss the Moser-Trudinger inequality in terms of the blow-up masses and get the existence of solutions in a non-coercive regime by means of a variational argument, which is based on some improved Moser-Trudinger inequalities.

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Aleks Jevnikar, Wen Yang. 2016-05-27. A mean field equation involving positively supported probability measures: blow-up phenomena and variational aspects. https://arxiv.org/abs/1605.08560

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