Fully nonlinear equations with Muckenhoupt weights and applications

David Jesus, Yannick Sire

Published 2023-07-22Version 1

We investigate the regularity of viscosity solutions for fully nonlinear Hessian equations with coefficients in some $A_p$ class. We prove H\"older and higher regularity under mild assumptions on the coefficients. We use approximation techniques in the spirit of Caffarelli's seminal approach. A special attention has to be paid to the degeneracy of the coefficients and we assume some natural structural assumptions which entail applications to curvature equations on conic manifolds.