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Nonlinear Analysis

The Alt-Phillips functional for negative powers

Speaker: Daniela De Silva, Barnard College

Location:  Hill 705
Date & time: Tuesday, 04 April 2023 at 1:40PM - 2:40PM

Abstract: We discuss the one-phase free boundary problem associated to the Alt-Phillips functional \[\int_\Omega (|
abla u|^2 + u^\gamma \chi_{\{u>0\}}) dx\]for \(\gamma \in (-2,0).\) We establish partial regularity results for the free boundary and discuss the rigidity of global minimizers when \(\gamma\) approaches the extreme of the admissible values. 

Seminar website:  Nonlinear Analysis Seminar    (