6 papers · 1 filter
On Brezis' First Open Problem: A Complete Solution
Liming Sun, Juncheng Wei, Wen Yang
In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a…
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…
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…
Prescribing -curvature on even-dimensional manifolds with conical singularities
Aleks Jevnikar, Yannick Sire, Wen Yang
On a -dimensional closed manifold we investigate the existence of prescribed -curvature metrics with conical singularities. We present here a general existence and multiplic…
Boundary spike-layer solutions of the singular Keller-Segel system: existence, profiles and stability
Jose A. Carrillo, Jingyu Li, Zhi-An Wang +1
This paper is concerned with the boundary-layer solutions of the singular Keller-Segel model proposed by Keller-Segel (1971) in a multi-dimensional domain, where the zero-flux boun…
Localization for general Helmholtz
Xinyu Cheng, Dong Li, Wen Yang
In \cite{gmw2022}, Guan, Murugan and Wei established the equivalence of the classical Helmholtz equation with a ``fractional Helmholtz" equation in which the Laplacian operator is…