An Aleksandrov-Bakelman Type Maximum Principle and Applications

Maximum Principle for Spdes and Its Applications

The maximum principle for SPDEs is established in multidimensional C domains. An application is given to proving the Hölder continuity up to the boundary of solutions of one-dimensional SPDEs. The maximum principle is one of the most powerful tools in the theory of second-order elliptic and parabolic partial differential equations. However, until now it did not play any significant role in the ...

Lp-Minkowski and Aleksandrov-Fenchel type inequalities

In this paper we establish the Lp-Minkowski inequality and Lp-Aleksandrov-Fenchel type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies, respectively. As applications, we get some related results. The paper new contributions that illustrate this duality of projection and intersection bodies will be presented. M.S.C. 2000: 52A40.

An Aleksandrov-type Estimate for a Parabolic Monge-ampère Equation

A classical result of Aleksandrov allows one to estimate the size of a convex function u at a point x in a bounded domain Ω in terms of the distance from x to the boundary of Ω if R Ω det Du dx < ∞. This estimate plays a prominent role in the existence and regularity theory of the Monge-Ampère equation. Jerison proved an extension of Aleksandrov’s result that provides a similar estimate, in som...

On Monge–Ampère type equations arising in optimal transportation problems

On Monge-Ampère Type Equations Arising In Optimal Transportation Problems Truyen Van Nguyen DOCTOR OF PHILOSOPHY Temple University, May, 2005 Professor Cristian E. Gutiérrez, Chair In this dissertation we study Monge-Ampère type equations arising in optimal transportation problems. We introduce notions of weak solutions, and prove the stability of solutions, the comparison principle and the ana...

An Aleksandrov Type Estimate for Α-convex Functions