November 17, 2021
14th Karl Stromberg Memorial Lecture to be presented Nov. 18
Nageswari Shanmugalingam, University of Cincinnati, will present the 14th Karl Stromberg Memorial Lecture titled "A Multitude of Formulations of Dirichlet Problem for Least Gradient Functional." This lecture is part of the Mathematics Department Women Lecture Series in celebration of the 50th anniversary of the Association for Women in Mathematics and will be presented from 2:30-3:20 p.m. Thursday, Nov. 18, in 101 Cardwell Hall. The lecture also will be streamed via YouTube Live.
The abstract for the lecture is: We are always trying to optimize things in practice: taking the shortest path, maximizing productivity, minimizing energy spent. A class of elliptic PDEs would have us minimizing energy. For example, when $1<p<\infty$, minimizing the energy $\int_\Omega |\nabla u|^p d\mu$ subject to some boundary constraint is equivalent to solving the problem $-\Delta_p u=0$ in $\Omega$ with Dirichlet boundary data. Solutions to this problem are now relatively well-understood. When $p=1$, the minimization problem becomes purely geometric, and is related to minimal surfaces. However, the corresponding Dirichlet type condition can fail for this problem. We will discuss various ways of re-formulating the Dirichlet problem to obtain reasonable solutions, even in weighted Euclidean settings.
The math department is a part of K-State's College of Arts and Sciences. To learn more about opportunities in math at K-State, visit the math department website.