Colloquium / Seminars
Topic:Singular Solutions to Some Semilinear Elliptic Equations: An Approach of Born-Infeld Approximation
Speaker:Dr. HSIEH Chia Yu
(Department of Mathematics, The Chinese University of Hong Kong)Date time:Dec. 10, 2019 14:00 - 15:00
Venue:SA223
Tea Party:Dec. 10, 2019 13:30 (SA205)
Abstract:
Abstract. We construct singular solutions to a semilinear elliptic equation with exponential nonlinearity on a bounded domain in 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).Download:Talk_1081210.pdf
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