FIRST SEMESTER
Elliptic Equations and Variational Problems (CM512)
CM512: Elliptic Equations and Variational Problems
Prof. Vicenţiu Rădulescu
Basic notions on Sobolev spaces: main properties and embedding theorems. The Lax-Milgram lemma and Garding’s inequality.
Lower and upper solutions. The linear case. Stable solutions, uniqueness results (the Kransoselskii and the Brezis-Oswald theorems).
The variational characterization of the method of lower and upper solutions.
Bifurcation problems. The Implicit Function Theorem and applications to nonlinear bifurcation problems. The Amman and the Crandall-Rabinowitz theorems.
Bibliography
V. Barbu,
Partial Differential Equations and Boundary Value Problems, Mathematics and its Applications
, vol. 441, Kluwer, 1998.
H. Brezis,
Analyse fonctionnelle
, Masson, Paris, 1992.
H. Brezis and L. Nirenberg,
Nonlinear Functional Analysis and Applications to Partial Differential Equations
, in preparation.
D. Gilbarg and N. Trudinger,
Elliptic Partial Differential Equations of Second Order
, Springer Verlag, 1983.
V. Radulescu,
http://www.inf.ucv.ro/~radulescu/articles/nonlpde.pdf