HAMILTON-JACOBI方程的超压缩性及相关不等式(英文)

HYPERCONTRACTIVITY OF HAMILTON-JACOBI EQUATIONS AND RELATED INEQUALITIES

本文主要研究了p≥ 2 的对数 Sobolev不等式与一般Hamilton Jacobi方程解的超压缩性的相关性。同时我们也建立极小卷积不等式与p 阶费用传输不等式之间的关系。

In this paper we mainly investigate that the logarithmic Sobolev inequalities for p≥2 are related to the hypercontractivity of the solutions of the general Hamiltion Jacobi equations. At the same time we also describe a clear relation between infimum convolution inequalities and transportation inequalities with p power cost.