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

Nonlocal gradient operators are basic elements of nonlocal vector calculus that play important roles in nonlocal modeling and analysis. In this work, we extend earlier analysis on nonlocal gradient operators. In particular, we study a nonlocal Dirichlet integral that is given by a quadratic energy functional based on nonlocal gradients. Our main finding, which differs from claims made in previo...