Work

Zero-extension convergence and Sobolev spaces on changing domains

Year: 2024

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2411.10827

Authors: Evseev, Nikita, Kampschulte, Malte, Menovschikov, Alexander

Institution: Okinawa Institute of Science and Technology Graduate University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Grantová Agentura České Republiky

Award: Variational approaches to dynamical problems in continuum mechanics

OpenAlex ID: W4404574649

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