MM595 – Equações Elípticas

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.

Referência Bibliográfica: 

  • Gilbarg, David; Trudinger, Neil S. Elliptic partial differential equations of second order. Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
  •  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.
  • Jost, Jürgen Partial differential equations. Third edition. Graduate Texts in Mathematics, 214. Springer, New York, 2013.
  •  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.

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