A perturbation result for a Neumann problem in a periodic domain

TL;DR

This paper demonstrates that solutions to a Neumann problem for the Laplace equation in a periodic domain depend real analytically on the domain shape, periodicity, boundary data, and boundary integral, providing a detailed sensitivity analysis.

Contribution

It establishes the real analyticity of the solution with respect to multiple parameters in a periodic Neumann problem, extending understanding of parameter dependence in PDEs.

Findings

Solution depends real analytically on domain shape

Solution depends real analytically on periodicity parameters

Solution depends real analytically on boundary data

Abstract

We consider a Neumann problem for the Laplace equation in a periodic domain. We prove that the solution depends real analytically on the shape of the domain, on the periodicity parameters, on the Neumann datum, and on its boundary integral.