### Abstract

If Ω is an unbounded domain in ℝ^{N} and p > N, the Sobolev space W^{1,p}(Ω) is not compactly embedded into L ^{∞}(Ω). Nevertheless, we prove that if Ω is a strip-like domain, then the subspace of W^{1,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 language | English |
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Pages (from-to) | 383-395 |

Number of pages | 13 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 141 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*,

*141*(2), 383-395. https://doi.org/10.1017/S0308210510000168

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

Research output: Contribution to journal › Article

*Proceedings of the Royal Society of Edinburgh Section A: Mathematics*, vol. 141, no. 2, pp. 383-395. https://doi.org/10.1017/S0308210510000168

}

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 -