Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-12T21:19:37.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Low-dimensional compact embeddings of symmetric Sobolev spaces with applications

Published online by Cambridge University Press:  04 April 2011

Francesca Faraci ,
Antonio Iannizzotto  and
Alexandru Kristály
Francesca Faraci
Affiliation:
Dipartimento di Matematica e Informatica, Universitá degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, [email protected]
Antonio Iannizzotto
Affiliation:
Dipartimento di Matematica e Informatica, Universitá degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, [email protected]
Alexandru Kristály
Affiliation:
Department of Economics, Babeş-Bolyai University, Str. Teodor Mihali, nr. 58–60, 400591 Cluj-Napoca, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

If Ω is an unbounded domain in ℝN and p > N, the Sobolev space W1,p(Ω) is not compactly embedded into L∈(Ω). Nevertheless, we prove that if Ω is a strip-like domain, then the subspace of W1,p(Ω) consisting of the cylindrically symmetric functions is compactly embedded into L∈(Ω). As an application, we study a Neumann problem involving the p-Laplacian operator and an oscillating nonlinearity, proving the existence of infinitely many weak solutions. Analogous results are obtained for the case of partial symmetry.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 2 , April 2011 , pp. 383 - 395
Copyright
Copyright © Royal Society of Edinburgh 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)