Abstract
We initiate the study of an evolution problem associated to a mean field type equation. In the present paper, we give a compactness result for solutions of a perturbed mean field type equation. Our method is based on blow-up analysis relying on integral estimates. This result will be used in Casteras (2013) to prove the convergence of a flow associated to a mean field type equation.
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Communicated by A. Malchiodi.
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Castéras, JB. A mean field type flow part I: compactness of solutions to a perturbed mean field type equation. Calc. Var. 53, 221–246 (2015). https://doi.org/10.1007/s00526-014-0746-5
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DOI: https://doi.org/10.1007/s00526-014-0746-5