Trudinger type inequalities in RN and their best exponents

Shinji Adachi, Kazunaga Tanaka

    Research output: Contribution to journalArticle

    153 Citations (Scopus)

    Abstract

    We study Trudinger type inequalities in RN and their best exponents αN. We show for α ε (0, αN), αN = NωN-1 1/(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
    Publication statusPublished - 2000

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    Exponent
    Unit Sphere
    Surface area
    Bounded Domain
    False

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

    Cite this

    Trudinger type inequalities in RN and their best exponents. / Adachi, Shinji; Tanaka, Kazunaga.

    In: Proceedings of the American Mathematical Society, Vol. 128, No. 7, 2000, p. 2051-2057.

    Research output: Contribution to journalArticle

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