ICTP Mathematics Seminar - Wednesday 4 July, at 16:00 hrs. (Edgar A. PIMENTEL)

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S  2018


Wednesday 4 July, at 16.00 hrs.




Edgard A. Pimentel  (PUC- Rio)




Title:
Geometric regularity for (nonlinear) PDEs


Abstract:
In this talk we examine the regularity theory of the solutions to a few 
examples of (nonlinear) PDEs. Arguing through a genuinely geometrical 
method, we produce regularity results in Sobolev and Hölder spaces, 
including some borderline cases. Our techniques relate a problem of 
interest to another one - for which a richer theory is available - by 
means of a geometric structure, e.g., a path. Ideally, information is 
transported along such a path, giving access to finer properties of the 
original equation. Our examples include elliptic and parabolic fully 
nonlinear problems, the Isaacs equation, degenerate examples and a 
double divergence model. We close the talk with a discussion on open 
problems and further directions of work.



VENUE:  Stasi Seminar Room (ICTP Leonardo da Vinci Building, first floor)