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John Villavert
University of Texas—Rio Grand Valley
Some Open Problems for Weighted Elliptic Equations
March 8, 2019
2-3 PM, PGH 646
Abstract
In this talk, we will examine a family of nonlinear elliptic partial differential equations
and closely related integral equations. The equations we consider play key roles in solving
several problems from analysis and geometry, and they also serve as basic models in physics.
We will discuss several key properties of non-negative solutions to the elliptic problems,
e.g., the sharp conditions governing their existence and their qualitative behavior, while
highlighting some of our recent methods for establishing such properties. We shall then motivate
the significance of these properties, especially in their connection to some open problems
such as the Lane-Emeden and Hardy-Littlewood-Sobolev conjectures.
David H. Wagner University of Houston
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Last modified: September 26 2017 - 05:42:22