Journal
ADVANCES IN MATHEMATICS
Volume 182, Issue 2, Pages 307-332Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/S0001-8708(03)00080-X
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We show that mass transportation methods provide an elementary and powerful approach to the study of certain functional inequalities with a geometric content, like sharp Sobolev or Gagliardo-Nirenberg inequalities. The Euclidean structure of R-n plays no role in our approach: we establish these inequalities, together with cases of equality, for an arbitrary norm. (C) 2003 Elsevier Inc. All rights reserved.
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