Boundary trace embedding theorems for variable exponent Sobolev spaces
By Xianling Fan. 2008
129 citations recorded by the source corpus.
We study boundary trace embedding theorems for variable exponent Sobolev space W1,p(⋅)(Ω). Let Ω be an open (bounded or unbounded) domain in RN satisfying strong local Lipschitz condition. Under the hypotheses that p∈L∞(Ω), 1⩽infp(x)⩽supp(x) N, we prove that there is a continuous boundary trace embedding W1,p(⋅)(Ω)→Lq(⋅)(∂Ω) provided q(⋅), a measurable function on ∂Ω, satisfies condition p(x)⩽q(x)⩽(N−1)p(x)N−p(x) for x∈∂Ω.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/07b17b5c11474f3f21102d26d84021a7d90c6d9a
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In Applied Mathematics
- Jan Vyb'iral
- P. Hasto
- Vicentiu D. Rădulescu
- Maria-Magdalena Boureanu
- Dušan D. Repovš
- Giuseppe Mingione
- Dachun Yang
- Zhijun Zhang
In Computational Theory and Mathematics
- P. Hasto
- Vicentiu D. Rădulescu
- Maria-Magdalena Boureanu
- Jan Vyb'iral
- Dušan D. Repovš
- Giuseppe Mingione
- Zhijun Zhang
- Anouar Bahrouni
In Mathematical Physics
- Jan Vyb'iral
- Vicentiu D. Rădulescu
- P. Hasto
- Maria-Magdalena Boureanu
- Dachun Yang
- H. Kempka
- Wen Yuan
- Kwok-Pun Ho
Citations in the corpus
- Local-to-global results in variable exponent spaces (2009, background): “Fan [18].”
- Anisotropic Neumann problems in Sobolev spaces with variable exponent (2012, methodology): “We refer the reader to [22] for more details regarding the extension of the classical trace to Lebesgue–Sobolev spaces with variable exponent.”
- SOBOLEV AND JAWERTH EMBEDDINGS FOR SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY (2009, background): “The reader may consult also [12], [19] and references given there for other versions of the trace embedding theorem for Sobolev spaces with varying integrability.”