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College of Liberal Arts and Sciences | Mathematics

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October 3, 2018 | 1:00 p.m. - 2:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Fernando Charro, Associate Professor, Wayne State University

Title: The Aleksandrov-Bakelman-Pucci Maximum Principle revisited. Applications

Abstract: The Aleksandrov-Bakelman-Pucci maximum principle is a crucial tool in Caffarelli’s proof of the Harnack inequality for fully nonlinear uniformly elliptic equations, and the doorstep to regularity theory. This estimate has a parabolic counterpart for uniformly parabolic fully nonlinear equations. 

In this series of talks we will discuss the classical ABP estimate and some of its more recent developments and applications. In particular we will show a proof, due to X. Cabre, of the classical isoperimetric inequality with the best constant using the ABP method, applied to an appropriate linear Neumann problem.

We will also discuss ABP estimates for other nonlinear, possibly degenerate, elliptic and parabolic equations that include p-Laplacian equations and Mean Curvature Flows among others. Time permitting, and depending on the interests of the audience, we will also consider the special cases of the infinity Laplacian, or the fractional Laplacian.

For more information about this event, please contact Department of Mathematics at 3135772479 or