Translator Disclaimer
2008 Sobolev inequalities with variable exponent attaining the values $1$ and $n$
Petteri Harjulehto, Peter Hästö
Publ. Mat. 52(2): 347-363 (2008).

Abstract

We study Sobolev embeddings in the Sobolev space $W^{1,p(\cdot)}(\Omega)$ with variable exponent satisfying $1\leqslant p(x) \leqslant n$. Since the exponent is allowed to reach the values $1$ and $n$, we need to introduce new techniques, combining weak- and strong-type estimates, and a new variable exponent target space scale which features a space of exponential type integrability instead of $L^\infty$ at the upper end.

Citation

Download Citation

Petteri Harjulehto. Peter Hästö. "Sobolev inequalities with variable exponent attaining the values $1$ and $n$." Publ. Mat. 52 (2) 347 - 363, 2008.

Information

Published: 2008
First available in Project Euclid: 5 August 2008

zbMATH: 1163.46022
MathSciNet: MR2436729

Subjects:
Primary: 46E35

Rights: Copyright © 2008 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.52 • No. 2 • 2008
Back to Top