Bernoulli problem for rough domains

TL;DR

This paper investigates the Bernoulli free boundary problem in rough domains, demonstrating through asymptotic analysis and numerical tests that solutions can be approximated by smoother domain solutions at second order.

Contribution

It introduces an asymptotic approximation method for the Bernoulli problem in rough domains and confirms its accuracy with numerical validation.

Findings

Solution approximates the non-rough Bernoulli problem at second order.

Asymptotic analysis provides effective approximation in rough domains.

Numerical tests validate theoretical asymptotic results.

Abstract

We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at order 2. Numerical tests confirm these theoretical results.