Use cases of Degenerate Elliptic Equations part6(Machine Learning 2024)

1. Higher Hölder regularity for mixed local and nonlocal degenerate elliptic equations(arXiv)

Author : Prashanta Garain, Erik Lindgren

Abstract : We consider equations involving a combination of local and nonlocal degenerate p-Laplace operators. The main contribution of the paper is almost Lipschitz regularity for the homogeneous equation and Hölder continuity with an explicit Hölder exponent in the general case. For certain parameters, our results also imply Hölder continuity of the gradient. In addition, we establish existence, uniqueness and local boundedness. The approach is based on an iteration in the spirit of Moser combined with an approximation method