In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct some new exact solutions for some nonlinear partial differential equations via the cubic nonlinear Klein Gordon equation and the modified Kawahara equation. As a result, new generalized Jacobi elliptic fun...

Iterative methods for solving linear systems arising from the discretization of elliptic/parabolic partial differential equations require the use of preconditioners to gain increased rates of convergence. Preconditioners arising from incomplete factorizations have been shown to be very effective. However, the recursiveness of these methods can offset these gains somewhat on a vector processor. ...

Motivated by the structure of the Dynamics Programming Equations relative to Controlled Diffusions we study the Dirichlet value boundary problem governed by quasi–degenerate elliptic partial differential equations of second order. Interior properties of the solution involved to the Maximum Principle are also considered in the paper. 2000 Mathematics Subject Classification: 35B50, 35B37, 49L25

My research work centers around two broad topics: The analysis of nonlinear Partial Differential Equations (PDE) of elliptic and parabolic type (mainly free boundary problems and reaction-diffusion equations) and the study of transport phenomena (particularly the connection between kinetic and hydrodynamic models). My main contributions are described below (preprints are available at http://www...

We describe several topics within the theory of linear and nonlinear second order elliptic Partial Differential Equations. Through elementary approaches, we first explain how elliptic and parabolic PDEs are related to central issues in Probability and Geometry. This leads to several concrete equations. We classify them and describe their regularity theories. After this, most of the paper focuse...

This paper deals with the L theory of linear elliptic partial differential equations with bounded measurable coefficients. We construct in two dimensions examples of weak and so-called very weak solutions, with critical integrability properties, both to isotropic equations and to equations in non-divergence form. These examples show that the general L theory, developed in [1],[24] and [2], cann...