On generalized Moser-Trudinger inequalities without boundary condition

Robert Černý

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 3, page 743-785
  • ISSN: 0011-4642

Abstract

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We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.

How to cite

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Černý, Robert. "On generalized Moser-Trudinger inequalities without boundary condition." Czechoslovak Mathematical Journal 62.3 (2012): 743-785. <http://eudml.org/doc/247042>.

@article{Černý2012,
abstract = {We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.},
author = {Černý, Robert},
journal = {Czechoslovak Mathematical Journal},
keywords = {Orlicz space; Orlicz-Sobolev space; embedding theorem; sharp constant; Moser-Trudinger inequality; concentration-compactness principle; Orlicz space; Orlicz-Sobolev space; embedding theorem; Moser-Trudinger inequality; concentration-compactness principle},
language = {eng},
number = {3},
pages = {743-785},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On generalized Moser-Trudinger inequalities without boundary condition},
url = {http://eudml.org/doc/247042},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Černý, Robert
TI - On generalized Moser-Trudinger inequalities without boundary condition
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 3
SP - 743
EP - 785
AB - We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.
LA - eng
KW - Orlicz space; Orlicz-Sobolev space; embedding theorem; sharp constant; Moser-Trudinger inequality; concentration-compactness principle; Orlicz space; Orlicz-Sobolev space; embedding theorem; Moser-Trudinger inequality; concentration-compactness principle
UR - http://eudml.org/doc/247042
ER -

References

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