Variational principles, Euler-Lagrange equation, existence of minimizers and/or saddle points, Palais-Smale condition, pseudo-gradient-flow, minimax-principles, applications to partial differential equations.
Learning objective
Characterization of solutions to certain partial differential equations as critical points of a suitable variational integral. Strategies for showing existence of critical points.
Content
Variational principles, Euler-Lagrange equation, existence of minimizers and/or saddle points, Palais-Smale condition, pseudo-gradient-flow, minimax-principles, applications to partial differential equations.
Literature
M. Struwe: Variational Methods, Springer, 4th edition, 2008
