In this note we prove a new symmetrization result, in the form of mass concentration comparison, for solutions nonlocal nonlinear Dirichlet problems involving fractional $ p Laplacians. Some regularity estimates will be established as direct application main result.

SUMMARY The nonlinear multigrid is an eecient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems 7],,9]. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble, et al. in 5], 6], and 17]. In particular, we prove the convergence of the n...

The present paper deals with a survey of numerical techniques for solving nonlinear elliptic singular perturbation problems, developed by numerous researchers in a chronological order as the field developed year after year from 1985. A large amount of research material related to nonlinear elliptic singularly perturbed problems has been collected with the aim of introduction to some of the idea...

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...