Tags » Maximum Principle

First Bourbaki seminar of 2015 (II): Carron's talk

For the second installment of this series of posts (which started here) on the first Bourbaki seminar of 2015, we will discuss Gilles Carron… 2,384 more words

Mathematics

Monge-Ampere equation and bounday behavior of domain

Suppose is a bounded domain and is . If there exists a convex function satisfies

Then is uniformly convex. In other words, the principle curvature  of every point on , namely , are positive. 151 more words

PDE

Improvement of Aleksandrov maximum principle

For we have

where .

There is an easy proof when the RHS is . We will adjust the original proof.

By replacing with , it suffices to assume on . 92 more words

PDE

Strong barrier function and generalized linear elliptic equation

Suppose is a domain in . satisfies the exterior sphere condition. That is there exists a ball such that . Then the function

is a barrier function for at . 111 more words

PDE

One simple maximum principle

If is elliptic with in a bounded domain , and satisfies in , then

Let

Then and on . By the maximum principle, we conclude, … 12 more words

PDE

Design, implementation, and experimental validation of optimal power split control for hybrid electric trucks

Hybrid electric vehicles require an algorithm that controls the power split between the internal combustion engine and electric machine(s), and the opening and closing of the clutch. 131 more words

Automotive & Mobility

The Payne's Maximum Principles

This note, completely based on the elegant paper of L.E. Payne [here], deals primarily with maximum principles for solutions of second order and fourth order elliptic equations. 611 more words

PDEs