We are concerned with the mean field equation with singular data on bounded domains. By assuming a singular point to be a critical point of the 1-vortex Kirchhoff-Routh function, we prove local uniqueness and non-degeneracy of bubbling solutions blowing up at a singular point. The proof is based on sharp estimates for bubbling solutions of singular mean field equations and a suitably defined Pohozaev-type identity. (C) 2020 Elsevier Inc. All rights reserved.
Bartolucci, D., Jevnikar, A., Lee, Y., Yang, W. (2020). Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data. JOURNAL OF DIFFERENTIAL EQUATIONS, 269(3), 2057-2090 [10.1016/j.jde.2020.01.030].
Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data
Bartolucci, Daniele
Membro del Collaboration Group
;
2020-01-01
Abstract
We are concerned with the mean field equation with singular data on bounded domains. By assuming a singular point to be a critical point of the 1-vortex Kirchhoff-Routh function, we prove local uniqueness and non-degeneracy of bubbling solutions blowing up at a singular point. The proof is based on sharp estimates for bubbling solutions of singular mean field equations and a suitably defined Pohozaev-type identity. (C) 2020 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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BJLY4 arXiv 1905.11749.pdf
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