The aim of this work is to develop a basic theory for nonlinear elliptic equations on long or thin domains for Dirichlet boundary conditions. This is the first treatment of such Dirichlet problems, which are of significant interest in applications.

Readership

Nonlinear partial differential equations experts and nonlinear analysts.

Table of Contents

• Introduction
• Limits of solutions on long bounded domains
• Construction of solutions from approximate solutions
• The end equation
• On the unstable solutions
• Some examples
• References