In this paper, by introducing an anisotropic tempered fractional $ p $-Laplacian operator (-\Delta)_{p, \lambda}^{\beta/2, m} $, based on the Laplacian \Delta_{m}^{\beta/2} and one \Delta_{m}^{\beta/2, \lambda} which are studied Deng et.al recently in [13], model involving logarithmic nonlinearity is considered. We first establish maximum principle boundary estimate, play a very crucial role la...

In this paper we find out the evolution formula for first nonzero eigenvalue of weighted p-Laplacian operator acting on space functions under Cotton flow a closed Riemannian 3-manifold M3.

The goal of this paper is to study a nonlinear elliptic equation in which the divergence form operator −div(a(x,∇u)) is involved. Such operators appear in many nonlinear diffusion problems, in particular in the mathematical modeling of non-Newtonian fluids (see [5] for a discussion of some physical background). Particularly, the p-Laplacian operator −div(|∇u|p−2∇u) is a special case of the oper...

Diffusion processes capture information about the geometry of an object such as its curvature, symmetries and particular points. The evolution of the diffusion is governed by the Laplace-Beltrami operator which presides to the diffusion on the manifold. In this paper, we define a new discrete adaptive Laplacian for digital objects, generalizing the operator defined on meshes. We study its eigen...

We consider the p-Laplacian in R perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p > d and p = d and discuss the connection with Sobolev interpolation inequalities. AMS Mathematics Subject Classification: 49R05, 35P30