Higher order Gamma-limits for singularly perturbed Dirichlet-Neumann problems

TL;DR

This paper investigates the asymptotic behavior of solutions to singularly perturbed Dirichlet-Neumann problems using Gamma-convergence, providing higher order Gamma-limits and extending classical results in the field.

Contribution

It introduces higher order Gamma-limits for singularly perturbed boundary problems, advancing the understanding of their asymptotic behavior as the perturbation parameter approaches zero.

Findings

Derived higher order Gamma-limits for the perturbed problems

Revealed detailed asymptotic behavior of solutions as epsilon tends to zero

Extended classical results with new asymptotic analysis techniques

Abstract

A mixed Dirichlet-Neumann problem is regularized with a family of singularly perturbed Neumann-Robin boundary problems, parametrized by $\varepsilon > 0$. Using an asymptotic development by Gamma-convergence, the asymptotic behavior of the solutions to the perturbed problems is studied as $\varepsilon \to 0^+$, recovering classical results in the literature.