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PDF(445 KB)
PDF(445 KB)
Sobolev—Lorentz范数约束下的次临界型Adams不等式
A Sharp Subcritical Adams Inequality in Lorentz Sobolev Space
本文在Sobolev—Lorentz空间W 2L2，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.
We obtain a sharp second order subcritical Adams inequality in Lorentz Sobolev space W 2L2,q(R4). Moreover, the lower and upper bounds asymptotically for the subcritical Adams functional is obtained. Our approach is based on the rearrangement free argument developed by Lam and Lu[A new approach to sharp MoserTrudinger and Adams type inequalities:a rearrangement-free argument, J. Diff. Equ., 2013, 255(3):298-325].
次临界 / Adams不等式 / Sobolev&mdash / Lorentz空间 / 重排理论 {{custom_keyword}} /
subcritical / Adams' inequality / Sobolev-Lorentz space / rearrangement argument {{custom_keyword}} /
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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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