Zero-extension convergence and Sobolev spaces on changing domains
Analysis of PDEs
2024-11-20 v2 Functional Analysis
Abstract
We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration. We then develop the respective theory and counterparts to classical compactness theorems from the fixed domain case. Finally, we illustrate the usefulness of these definitions with some examples from applications and compare them to other approaches.
Cite
@article{arxiv.2411.10827,
title = {Zero-extension convergence and Sobolev spaces on changing domains},
author = {Nikita Evseev and Malte Kampschulte and Alexander Menovschikov},
journal= {arXiv preprint arXiv:2411.10827},
year = {2024}
}