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On $C^{2,\alpha}$ estimates for levels sets of Allen-Cahn equation

Jun-Cheng Wei, University of British Columbia
Friday, December 6, 2019 - 2:30pm to 3:30pm
SMI 205
Jun-cheng Wei, University of British Columbia

I will discuss recent new developments in De Giorgi Conjecture for Allen-Cahn equation. In dimensions up to 10, we shall establish the \$C^{2,\alpha}\$ estimates of level sets for stable solutions of Allen-Cahn. By applying reverse gluing method we show that the obstruction to \$C^{2,\alpha}\$ estimates is the existence of Toda System in one dimension less. Applications to classifications of finite Morse index solutions and some open problems will be discussed.

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