A local proof of the dimensional Prekopa's theorem

作者：Van Hoang Nguyen^*

来源：Journal of Mathematical Analysis and Applications, 2014, 419(1): 20-27.

DOI：10.1016/j.jmaa.2014.04.045

• Prekopa's theorem
• Dimensional Prekopa's theorem
• L-2-method

The aim of this paper is to find an expression for second derivative of the function phi(t) defined by
phi(t) = (integral(V)phi(t, x)(-beta) dx)(-1/beta-n), beta not equal n,
where U subset of R and V subset of R-n are open bounded subsets, and phi : U x V -> R+ is a C-2-smooth function. As a consequence, this result gives us a direct proof of the dimensional Prekopa's theorem based on a local approach.

• 出版日期2014-11-1