Interpolation inequalities on the sphere: linear vs. nonlinear flows
Interpolation inequalities on the sphere: linear vs. nonlinear flows
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球体上的插值不等式：线性流与非线性流
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Loss
中科院分区：
文献类型：
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作者：
J. Dolbeault;M. Esteban;M. Loss
本文研究了球面上的尖锐插值不等式及其流的证明。该方法解释了一些刚性结果，并证明了相关半线性椭圆方程的唯一性。非线性流动允许覆盖从庞加莱不等式到索博列夫不等式的指数区间，而一个有趣的限制（指数的上界）出现在基于热流的卡尔杜champ方法中。我们研究了这个限制，描述了一个指数在界以上的反例，并在下面得到改进。
This paper is devoted to sharp interpolation inequalities on the sphere and their proof using flows. The method explains some rigidity results and proves uniqueness in related semilinear elliptic equations. Nonlinear flows allow to cover the interval of exponents ranging from Poincar'e to Sobolev inequality, while an intriguing limitation (an upper bound on the exponent) appears in the carr'e du champ method based on the heat flow. We investigate this limitation, describe a counter-example for exponents which are above the bound, and obtain improvements below.