A Singular Moser-Trudinger Inequality on Metric Measure Space

IF 0.3 4区 数学 Q4 MATHEMATICS, APPLIED Journal of Partial Differential Equations Pub Date : 2022-06-01 DOI:10.4208/jpde.v35.n4.3
Yaoting Gui
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Abstract

. Let ( X , d , µ ) be a metric space with a Borel-measure µ , suppose µ satisfies the Ahlfors-regular condition, i.e. where b 1 , b 2 are two positive constants and s is the volume growth exponent. In this paper, we mainly study two things, one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that s is not less than 2. The other is to study the generalized Moser-Trudinger inequality with a singular weight.
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度量测度空间上的一个奇异Moser-Trudinger不等式
. 设(X, d,µ)为具有borel -测度µ的度量空间,设µ满足ahlfors -正则条件,即b1, b2为两个正常数,s为体积增长指数。本文主要研究两点,一是考虑s不小于2条件下度量空间上Moser-Trudinger不等式的最佳常数。二是研究具有奇异权的广义Moser-Trudinger不等式。
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