Fully nonlinear elliptic PDEs in thin domains with oblique-Dirichlet mixed boundary conditions

TL;DR

This paper studies the asymptotic behavior of solutions to fully nonlinear elliptic PDEs with oblique-Dirichlet boundary conditions in thin domains, introducing a global ellipticity condition for the limit equation.

Contribution

It analyzes the asymptotics of nonlinear elliptic PDEs in collapsing thin domains without requiring strict monotonicity, and introduces a global ellipticity condition for the limit.

Findings

Established asymptotic behavior of solutions in thin domains

Introduced a global ellipticity condition for the limit equation

Analyzed PDEs without strict monotonicity in the unknown variable

Abstract

We consider asymptotic behavior of solutions to the oblique-Dirichlet mixed boundary conditions without the strict monotonicity of the equation in the variable corresponding to the unknown function for "thin domains" i.e. when the N+1 dimensional domains collapse to an N dimensional domain. A global ellipticity condition in the limit equation is introduced.