An Iteration Method for Solving Elliptic Equations

TL;DR

This paper introduces an iteration method to prove the existence of solutions for nonlinear elliptic equations, including the prescribed mean curvature equation, with applications to unbounded domains.

Contribution

It presents a natural iteration technique that extends to unbounded domains, providing a new approach for solving nonlinear elliptic boundary value problems.

Findings

Proves existence of solutions for nonlinear Dirichlet problems.

Applies to unbounded domains such as ^{n-1} imes (-d/2, d/2).

Includes examples like the prescribed mean curvature equation.

Abstract

In this paper we use a natural iteration technique to prove existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to unbounded domains, as we show with domains of the form $\mathbb{R}^{n-1}\times\left(-d/2,d/2\right)$.