TY - JOUR
T1 - Trudinger type inequalities in RN and their best exponents
AU - Adachi, Shinji
AU - Tanaka, Kazunaga
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
SN - 0002-9939
VL - 128
SP - 2051
EP - 2057
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -