Almost minimizers for obstacle problems
Mariana Smit Vega Garcia (Western Washington University)
Abstract: In the applied sciences one is often confronted with free boundaries, which arise when the solution to a problem consists of a pair: a function u (often satisfying a partial differential equation), and a set where this function has a specific behavior. Two central issues in the study of free boundary problems are:
(1) What is the optimal regularity of the solution u?
(2) How smooth is the free boundary?
The study of the classical obstacle problem - one of the most renowned free boundary problems - began in the ’60s with the pioneering works of G. Stampacchia, H. Lewy, and J. L. Lions. During the past decades, it has led to beautiful developments, and its study still presents very interesting and challenging questions. In contrast to the classical obstacle problem, which arises from a minimization problem (as many other PDEs do), minimizing problems with noise lead to the notion of almost minimizers. In this talk, I will introduce obstacle type problems and overview recent developments in almost minimizers for the thin obstacle problem, illustrating techniques that can be used to tackle questions (1) and (2) in various settings. This is joint work with Seongmin Jeon and Arshak Petrosyan.
analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry
Audience: researchers in the topic
Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.
Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.
| Organizers: | Bruno Poggi*, Ryan Matzke, Jose Luis Luna Garcia* |
| *contact for this listing |