Alberto Saldaña
CAMGSD - Instituto Superior Técnico

Abstract: Maximum principles are one of the most powerful tools in the analysis of linear and nonlinear elliptic partial differential equations. In particular, they guarantee that a solution of an equation inherits the sign of the data of the problem, this can be used, for example, to show symmetry properties of solutions, regularity, a priori bounds, existence and nonexistence of solutions. It is well known that higher-order operators do not satisfy in general maximum principles. In this talk we focus on positivity preserving properties for higher-order fractional powers of the Laplacian. We discuss counterexamples and some positive results. The aim of this talk is to be introductory and as much self-contained as possible.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.