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Nonlinear Analysis

A spiral interface with positive Alt-Caffarelli-Friedman limit at the origin

Dennis Kriventsov, Rutgers University

Location:  Hill 705
Date & time: Tuesday, 03 December 2019 at 1:40PM - 2:50PM

Abstract:   I will discuss an example of a pair of continuous nonnegative subharmonic functions, each vanishing where the other is positive, which have a strictly positive limit for the Alt-Caffarelli-Friedman monotonicity formula at the origin, but for which the origin is not a point of differentiability for the boundary of their supports. Time permitting, I will also discuss some further progress on related problems.

This is based on joint work with Mark Allen.