Title: Graphical solutions to one-phase problems

Speaker: Hui Yu (National University of Singapore)

Time and venue: 14:30-15:30, May 25th, 2023, 公共教学四楼4106

Abstract: Free boundaries of solutions to the one-phase problem can have rich geometry. Such richness can be reduced by imposing the graphical condition. In this talk, we show that if homogeneous minimizers are trivial in dimension k, then graphical solutions are trivial in dimension k+1. This works for both the classical one-phase problem as well as its thin counterpart. This talk is based on a joint work with Max Engelstein (Minnesota) and Xavier Fernandez-Real (EPFL).

About the speaker: Hui Yu is now a Presidential Young Professor at National University of Singapore. After receiving his PhD from University of Texas at Austin under the direction of Prof. Luis A. Caffarelli, he became a Ritt Assistant Professor at Columbia University. He works in theory of elliptic PDEs, calculus of variations and geometric flows. His works have been published in journals such as Communications on Pure and Applied Mathematics, Duke Mathematical Journal, J. European Math Society, and Archive for Rational Mechanics and Analysis.