A degenerate fully nonlinear free transmission problem with variable exponents
arXiv:2111.02225
Abstract
We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating our problem to a homogeneous, fully nonlinear, uniformly elliptic equation.
31 pages, 0 figures. To be published in Calc. Var. Partial Differential Equations