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K-State Today Student Edition

September 27, 2017

ADVANCE Distinguished Lecture Series and Mathematics Colloquium lecture present Nages Shanmugalingam

By Tawny Ochs

The ADVANCE Distinguished Lecture Series, Mathematics Colloquium lecture and Lizaveta Ihnatsyeva, assistant professor of mathematics, will host Nages Shanmugalingam, University of Cincinnati, at 2:30 p.m. Thursday, Sept. 28, in 122 Cardwell Hall.

Shanmugalingam will present "What Does the Dirichlet Condition Mean for the Least Gradient Problem?"

Abstract: Least gradient functions are intimately connected to minimal surfaces. Unlike p-harmonic functions, the 1-harmonic functions — least gradient functions — do not have the Kellogg property for the Dirichlet problem. Given a domain and a Lipschitz function defined on the boundary of the domain, its least-gradient extension may not have the correct trace at the boundary. The difficulty here is in the formulation of the Dirichlet condition for this problem. The focus of this talk is to describe three possible formulations of the Dirichlet problem in this setting.