演講者：謝佳佑 博士 (香港中文大學數學系)

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

時間：12月10日上午11點

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).