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演講者: 謝佳佑 博士 (香港中文大學數學系)

講題:Singular Solutions to Some Semilinear Elliptic Equations: An Approach of Born-Infeld Approximation

時間:12/10(二) 11:00

地點:校本部第二綜合大樓8樓B808教室

摘要: We construct singular solutions to a semilinear elliptic equation with exponential nonlinearity on a bounded domain in $\mathbb{R}^2$. To show the existence of singular solutions, we introduce an inverse problem  and utilize a Born-Infeld approximation scheme. Ruling out a possible occurrence of bubbling phenomenon, we show that  as the Born-Infeld parameter tends to infinity, solutions of the inverse problem on a subdomain with finitely many  holes can be used to approximate singular solutions to the original problem. Our work rigorously justifies the  Born-Infeld-Higgs approximation to the abelian Maxwell-Higgs theory. This is a joint work with Yong Yu and Ho Man Tai (CUHK).

 

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