Parabolic Obstacle Problems. Quasi-convexity and Regularity
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
TL;DR
This paper investigates parabolic obstacle problems, demonstrating improved solution regularity and establishing space-time regularity of free boundaries, advancing understanding of these complex mathematical phenomena.
Contribution
It introduces methods to enhance regularity results for solutions and free boundaries in parabolic obstacle problems.
Findings
Improved optimal regularity of solutions.
Established space-time regularity of free boundaries.
Applicable to a broad class of parabolic obstacle problems.
Abstract
In a wide class of the so called Obstacle Problems of parabolic type it is shown how to improve the optimal regularity of the solution and as a consequence how to obtain space-time regularity of the corresponding free boundary.
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