Sobolev—Lorentz范数约束下的次临界型Adams不等式

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Sobolev—Lorentz范数约束下的次临界型Adams不等式朱茂春, 刘宇航江苏大学数学科学学院镇江 212013 A Sharp Subcritical Adams Inequality in Lorentz Sobolev Space Mao Chun ZHU, Yu Hang LIUSchool of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China

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摘要本文在Sobolev—Lorentz空间W ²L^2，q（R⁴）的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步，当次临界指标逼近最佳常数时，得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser—Trudinger and Adams type inequalities：a rearrangement-free argument，J. Diff. Equ.，2013，255（3）：298—325]的分割水平集方法.

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收稿日期: 2020-04-01

MR (2010):

O178

基金资助:国家自然科学基金资助项目（11601190，11701162，11661006）；江苏省青年基金资助项目（BK20160483）；江苏大学基础基金资助项目（16JDG043）

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朱茂春, 刘宇航. Sobolev—Lorentz范数约束下的次临界型Adams不等式[J]. 数学学报, 2021, 64(2): 231-242. Mao Chun ZHU, Yu Hang LIU. A Sharp Subcritical Adams Inequality in Lorentz Sobolev Space. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 231-242.

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