Kim, Sunghan: Sharp Regularity of Solutions to (p)-Parabolic Obstacle Problems under Interpolative Intrinsic Geometry.

Date: 2024-05-21

Time: 10:30 - 11:00

Zoom link:

Sunghan Kim, University of Uppsala


This talk is concerned with recent developments in the regularity theory regarding \(p\)-parabolic obstacle problems, where solutions are given as the minimal \(p\)-supercaloric functions above a given obstacle. Analyzing \(p\)-parabolic problems, even without obstacles, is notoriously difficult due to the lack of a strong minimum principle. As demonstrated by the Barenblatt solutions, nonnegative, nontrivial solutions to \(p\)-parabolic problems exist. DiBenedetto-Gianazza-Vespri overcame this issue through the invention of the intrinsic Harnack inequality. Subsequently, Kuusi-Mingione-Nyström applied this idea to the corresponding obstacle problem and obtained sharp (up-to-)Lipschitz estimates. Recently, Nyström and I extended this result to the higher-order regularity regime, by introducing new (optimal) intrinsic geometry upon which the solutions behave as regularly as the obstacle, near the free boundaries. This talk will be based on our recent joint work with K. Nyström.