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math.AP2024
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
Daniele Bartolucci, Wen Yang, Lei Zhang
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 e…
math.AP2024
Sharp estimates, uniqueness and spikes condensation for superlinear free boundary problems arising in plasma physics
Daniele Bartolucci, Aleks Jevnikar, Ruijun Wu
We are concerned with Grad-Shafranov type equations, describing in dimension the equilibrium configurations of a plasma in a Tokamak. We obtain a sharp superlinear generaliza…
math.AP2024
Asymptotic Analysis and Uniqueness of blowup solutions of non-quantized singular mean field equations
Daniele Bartolucci, Wen Yang, Lei Zhang
For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quant…