Higher Holder regularity for mixed local and nonlocal degenerate elliptic equations

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 Holder continuity with an explicit Holder exponent in the general case. For certain parameters, our results also imply Holder 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.