Banca de DEFESA: CARLOS EDUARDO SOARES DE MARIA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : CARLOS EDUARDO SOARES DE MARIA
DATE: 26/08/2022
TIME: 14:00
LOCAL: Google Meet
TITLE:

f-extremal domains for the Laplacian operator

KEY WORDS:

Extremal domains; overdetermined problems; maximum principle; moving plane method.

PAGES: 67
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Geometria e Topologia
SPECIALTY: Geometria Diferencial
SUMMARY:

In this dissertation, we investigate geometric properties of extremal domains, bounded or not. The extremal domains are the domains that are critical points for the first eigenvalue functional for volume-preserving variations.
We show that these domains are characterized by admitting a non-trivial solution to an overdetermined Serrin-type problem.
This motivates us to define the f-extremal domains, when we use an arbitrary function f as the nonlinearity of the overdetermined problem.
The main tool used is the maximum principle in the format of the moving planes method and the main result is the Ros-Sicbaldi Theorem on the proof of Berestycki-Caffarelli-Nirenberg Conjecture in dimension two when the nonlinearity grows at least as a function linear.

BANKING MEMBERS:
Presidente - 1435426 - MARCOS PETRUCIO DE ALMEIDA CAVALCANTE
Interno - 2474631 - MARCIO HENRIQUE BATISTA DA SILVA
Externo à Instituição - JOSÉ NAZARENO VIEIRA GOMES - UFSCAR