MM595 - Equações Elípticas - 2S/2026 Imprimir

Ementa:

Equações elípticas lineares, na forma do divergente e quase-lineares. O problema de Dirichlet. Desigualdade de Harnak. Princípios de máximo. Estimativas do gradiente. Soluções fracas e soluções clássicas. Teoria de regularidade de Schauder. Regularidade no interior e até a fronteira do domínio. Teoria de regularidade Lp.

Bibliografia:

1. Gilbarg, David; Trudinger, Neil S. Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
2. Han, Qing; Lin, Fanghua Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011.
3. Jost, Jürgen Partial differential equations. Third edition. Graduate Texts in Mathematics, 214. Springer, New York, 2013.
4. Ladyzhenskaya, Olga A.; Uralt'seva, Nina N. Linear and Quasilinear Elliptic Equations, Mathematics in Science and Engineering 46, New York and London: Academic Press, 1968;
5. Fernández-Real, Xavier and Ros-Oton, Xavier Regularity theory for elliptic PDE. Zur. Lect. Adv. Math., 28. EMS Press, Berlin, [2022], ©2022. viii+228 pp.;
6. Han, Qing, Nonlinear elliptic equations of the second order. Grad. Stud. Math., 171. American Mathematical Society, Providence, RI, 2016. viii+368 pp.;
7. da Silva, João Vitor and Ricarte, Gleydson, Regularidade elíptica e problemas de fronteiras livres.(Portuguese)[Elliptic regularity and free boundary problems] 34 o Colóq. Bras. Mat., 8 Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 2023. 156 pp.;
8. Katzourakis, Nikos,  An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L^∞. SpringerBriefs Math. Springer, Cham, 2015. xii+123 pp.

Ano de Catálogo: 2026

Créditos: 4