The game-theoretic p-Laplacian operator is a version of classical variational which in connection with stochastic games called Tug-of-War noise. existence positive singular and Holder continuous solutions the p-Laplace involving gradient small C2 perturbation unit ball Rn are proved. Finally, more case problem introduced.

We consider traveling wave solutions to a class of diierential-diierence equations. Our interest is in understanding propagation failure, directional dependence due to the discrete Laplacian, and the relationship between traveling wave solutions of the spatially continuous and spatially discrete limits of this equation. The diierential-diierence equations that we study include damped and undamp...

Let (M, g) be a pseudo-Riemannian manifold and Fλ(M) the space of densities of degree λ on M . We study the space D2 λ,μ(M) of second-order differential operators from Fλ(M) to Fμ(M). If (M, g) is conformally flat with signature p− q, then D2 λ,μ(M) is viewed as a module over the group of conformal transformations of M . We prove that, for almost all values of μ− λ, the O(p+1, q+1)-modules D2 λ...

In this paper we continue the study of functional calculus for the Laplace{ Beltrami operator on symmetric spaces of the noncompact type begun in 3]; this paper is dedicated to a study of the Poisson semigroup, which we deene shortly. Let G and K be a connected noncompact semisimple Lie group with nite center and a maximal compact subgroup thereof, and consider the symmetric space G=K; also den...