Trudinger type inequalities in RN and their best exponents

Shinji Adachi, Kazunaga Tanaka

Research output: Contribution to journalArticle

177 Citations (Scopus)

Abstract

We study Trudinger type inequalities in RN and their best exponents αN. We show for α ε (0, αN), αN = NωN-11/(N-1)N-1 is the surface area of the unit sphere in RN), there exists a constant Cα > 0 such that (Equation Presented) for all u 6 ε W1,N(RN) \ {0}. Here ΦN(ε) is defined by (Equation Presented) It is also shown that (*) with α ≥ αN is false, which is different from the usual Trudinger's inequalities in bounded domains.

Original languageEnglish
Pages (from-to)2051-2057
Number of pages7
JournalProceedings of the American Mathematical Society
Volume128
Issue number7
DOIs
Publication statusPublished - 2000 Jan 1

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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