Workshop

Data evento: 
Mercoledì, 30 Gennaio, 2019 - 15:00
Analisi MaTÈmatica allo SBAI
Dipartimento SBAI, Sapienza
Aula Seminari
 
Mercoledì 30 Gennaio 2019
Ore 15: Seunghyeok Kim (Hanyang University)
 
 Elliptic systems with nearly critical exponents on general domains
 
Abstract: In 2008, Guerra studied the asymptotic behavior of positive minimal energy solutions 
of nearly critical Lane-Emden systems on smooth bounded convex domains, 
as the exponents of the nonlinear terms approach the critical Sobolev hyperbola. 
In his work, in addition to the convexity assumptions on domains, 
there was a restriction on the range of the exponents. 
In this talk, we remove all these technical assumptions, 
thereby completing the analysis under the whole subcritical regime. 
This is a joint work with Professor Woocheol Choi (Incheon National University).
 
 
Ore 16: Michał Łasica (University of Warsaw)
Existence of 1-harmonic map flow 
 
Given a complete Riemannian manifold, we consider the problem of constructing an L2-steepest descent flow of the total variation energy of maps taking values in the manifold. In the case that the domain is a convex, bounded subset of a Euclidean space or a compact, orientable Riemannian manifold, we are able to prove local existence of a suitably defined flow on Lipschitz maps, which under some conditions can be continued indefinitely. This flow is unique. If the domain is an interval, we can define and construct a globally existing flow on maps (parametrized curves) of bounded variation. If the target manifold has non-positive sectional curvatures, this flow coincides with the one obtained by the general construction of Ambrosio, Gigli, Savare and is unique.