Non degeneracy of blow-up solutions of non-quantized singular Liouville-type equations and the convexity of the mean field entropy of the Onsager vortex model with singular sources
Abstract
We establish the non-degeneracy of bubbling solutions for singular mean field equations when the blow-up points are either regular or involve non-quantized singular sources. This extends the results from Bartolucci-Jevnikar-Lee-Yang bart-5, which focused on regular blow-up points. As a consequence, we establish the strict convexity of the Entropy in the large energy limit for a specific class of two-dimensional domains in the Onsager mean field vortex model with singular sources.
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