Low-dimensional compact embeddings of symmetric Sobolev spaces with applications

Francesca Faraci, Antonio Iannizzotto, A. Kristály

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)383-395
Number of pages13
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume141
Issue number2
DOIs
Publication statusPublished - Apr 2011

Fingerprint

Compact Embedding
Symmetric Spaces
Sobolev Spaces
P-Laplacian Operator
Neumann Problem
Symmetric Functions
Unbounded Domain
Weak Solution
Strip
Subspace
Nonlinearity
Partial
Symmetry

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Low-dimensional compact embeddings of symmetric Sobolev spaces with applications. / Faraci, Francesca; Iannizzotto, Antonio; Kristály, A.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 141, No. 2, 04.2011, p. 383-395.

Research output: Contribution to journalArticle

@article{433eda7f9164470789993cd848493246,
title = "Low-dimensional compact embeddings of symmetric Sobolev spaces with applications",
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.",
author = "Francesca Faraci and Antonio Iannizzotto and A. Krist{\'a}ly",
year = "2011",
month = "4",
doi = "10.1017/S0308210510000168",
language = "English",
volume = "141",
pages = "383--395",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - Low-dimensional compact embeddings of symmetric Sobolev spaces with applications

AU - Faraci, Francesca

AU - Iannizzotto, Antonio

AU - Kristály, A.

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79960367890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960367890&partnerID=8YFLogxK

U2 - 10.1017/S0308210510000168

DO - 10.1017/S0308210510000168

M3 - Article

AN - SCOPUS:79960367890

VL - 141

SP - 383

EP - 395

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -