In this talk we will give a comprehensive overview of some classes of two-penalty boundary obstacle problems, motivated by applications to fluid dynamics and thermics. Specifically, we prove existence, uniqueness and optimal regularity of solutions, and establish structural properties of the free boundary. The proofs are based on tailor-made monotonicity formulas of Almgren, Weiss, and Monneau-type, combined with the classical theory of oblique derivative problems.
Regularity results for a class of penalized boundary obstacle problems
Donatella Danielli, Arizona State University
2023 AWM Research Symposium
Advances in Partial Differential Equations and Applications [Organized by Maya Chhetri, Nsoki Mavinga and Irina Mitrea]