Speaker
Dr
Rafayel Teymurazyan
(KAUST)
Description
We present recent advances on the degenerate quenching problem. Our main result establishes the local finiteness of the (n-1)-dimensional Hausdorff measure of the free boundary. The proof combines optimal gradient decay estimates, derived from an intrinsic Harnack-type inequality, with a detailed analysis of the flatness regime, where minimizers enjoy improved regularity. This approach yields an alternative proof of the classical results of Phillips and, although developed in the degenerate setting, provides insights relevant to the singular case. Furthermore, we prove that, as in the linear setting, the free boundary is rectifiable.
Author
Dr
Rafayel Teymurazyan
(KAUST)
Co-authors
Damião J. Araujo
(Universidade Federal da Paraíba)
José Miguel Urbano
(KAUST)