Special Session 82: Recent Advances in Nonlinear PDEs and Free Boundary Problems
Sharp regularity for singular/degenerate fully nonlinear free boundary problems with singular absorption terms
Seunghyun Kim
Seoul National University Korea
Co-Author(s): Jose Miguel Urbano
Abstract:
We investigate the sharp local regularity of viscosity solutions to singular or degenerate fully nonlinear elliptic free boundary problems with singular absorption terms. By employing suitable substitutions and the Ishii-Lions method, we establish regularity estimates for the associated auxiliary problems. Additionally, we explore the parabolic case.