Small Perturbation Solutions for Elliptic Equations

Small Perturbation Solutions for Elliptic Equations

In this work we present a general regularity result for small perturbation solutions of elliptic equations. Our approach was motivated by the analysis of flat level sets in Ginzburg-Landau phase transitions models, which were considered in Savin (2003). When dealing with uniformly elliptic equations of the form (1), the classical approach to regularity is to differentiate the equation with resp...

Elliptic Hypergeometric Solutions to Elliptic Difference Equations⋆

It is shown how to define difference equations on particular lattices {xn}, n ∈ Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.

Asymptotic Solutions of Singular Perturbation Problems for Linear Differential Equations of Elliptic Type

Singular Solutions for some Semilinear Elliptic Equations

We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.