Tese de Doutorado – Christopher Silva Aguiar

Título: Qualitative properties and strong maximum principles for degenerate and singular fully nonlinear elliptic operators

Resumo: This thesis focuses on two classes of problems. First, we develop a new strategy to prove the strong maximum principle for equations governed by linear operators in non-divergence form. The analysis is carried out in a setting where the lower-order coefficients may be unbounded and the right-hand side of the equation is allowed to be nonhomogeneous under optimal assumptions. The second part of the thesis addresses qualitative properties of supersolutions to singular and degenerate operators. In this context, we recover both the strong maximum principle and the compact support principle under new optimal assumptions on the right-hand side. Moreover, we establish regularity estimates for semiconvex supersolutions corresponding to a given modulus of continuity.

Banca Examinadora:
Orientador: Boyan Slavchev Sirakov - PUC-Rio

Banca examinadora:
Gabrielle Saller Nornberg - UChile
Edgard Almeida Pimentel - Universidade de Coimbra
Makson Sales Santos - Universidade de Lisboa
Disson Soares dos Prazeres - UFS
Julio Cesar Correa Hoyos - UERJ
Aelson Oliveira Sobral - KAUST

Data: 30/04/2026
Horário: 9h30
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