Free boundary regularity in obstacle problems
Alessio Figalli
TL;DR
This paper reviews the classical theory of obstacle problems and discusses recent advances in understanding the regularity of the free boundary, highlighting developments since the original lectures in 2018.
Contribution
It provides an overview of classical obstacle problem theory and introduces recent progress on free boundary regularity, expanding the existing literature.
Findings
Summary of classical obstacle problem theory
Recent results on free boundary regularity
Enhanced understanding of free boundary smoothness
Abstract
These notes record and expand the lectures for the `Journ\'ees \'Equations aux D\'eriv\'ees Partielles 2018' held by the author during the week of June 11-15, 2018. The aim is to give a overview of the classical theory for the obstacle problem, and then present some recent developments on the regularity of the free boundary.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering