Low-dimensional compact embeddings of symmetric Sobolev spaces with applications
Published online by Cambridge University Press: 04 April 2011
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
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