For an elliptic equation with the p(x)-Laplacian, where exponent p(∙) is a bounded measurable function, we find conditions guaranteeing continuity of solution at point.

Solving optimal control problems for real world applications are hard to tackle numerically due to the large size and the complex underlying (partial differential equations based) models. In this paper a structural optimization problem governed by the p-Laplace equation (fine model) is considered. A surrogate optimization is utilized to develop an efficient numerical optimization method. Here t...

We derive regularity estimates for viscosity solutions to the parabolic normalized p-Laplace. By using approximation methods and scaling arguments p-parabolic operator, we show that gradient of bounded is locally asymptotically Lipschitz continuous when p sufficiently close 2. In addition, establish in Sobolev spaces.

We prove novel (local) square function/Carleson measure estimates for non-negative solutions to the evolutionary $ p $-Laplace equation in complement of parabolic Ahlfors-David regular sets. In case heat equation, Laplace as well corresponding function have proven fundamental symmetry and inverse/free boundary type problems, particular study (parabolic) uniform rectifiability. Though implicatio...

Ergodicity for local and nonlocal stochastic singular p-Laplace equations is proven, without restriction on the spatial dimension and for all p ∈ [1, 2). This generalizes previous results from [Gess, Tölle; JMPA, 2014], [Liu, Tölle; ECP, 2011], [Liu; JEE, 2009]. In particular, the results include the multivalued case of the stochastic (nonlocal) total variation flow, which solves an open proble...