TY - JOUR

T1 - Trudinger type inequalities in RN and their best exponents

AU - Adachi, Shinji

AU - Tanaka, Kazunaga

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - We study Trudinger type inequalities in RN and their best exponents αN. We show for α ε (0, αN), αN = NωN-11/(N-1) (ωN-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.

AB - We study Trudinger type inequalities in RN and their best exponents αN. We show for α ε (0, αN), αN = NωN-11/(N-1) (ωN-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.

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U2 - 10.1090/s0002-9939-99-05180-1

DO - 10.1090/s0002-9939-99-05180-1

M3 - Article

AN - SCOPUS:23044521004

VL - 128

SP - 2051

EP - 2057

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 7

ER -