Teachers

Elisa Davoli
e-mail: elisa.davoliunivie.ac.at
webpage: http://www.mat.univie.ac.at/~davoli

Paolo Piovano
e-mail: paolo.piovanounivie.ac.at
webpage: http://www.mat.univie.ac.at/~piovano

Ulisse Stefanelli
e-mail: ulisse.stefanelliunivie.ac.at
webpage: http://www.mat.univie.ac.at/~stefanelli

Schedule

Montag 11:30 - 13:45, SR4
Oskar-Morgenstern-Platz 1.
Erster Temin/Vorbesprechung am 5.3

Aims

This is an introductory course in classical and modern methods in the Calculus of Variations. Topics will include: Direct Method, Euler-Lagrange equations, variational convergence, minimax problems.

Literature

• A. Ambrosetti, A. Malchiodi. Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge University Press, 2010.
• A. Braides. Gamma Convergence for Beginners, Oxford University Press, 2002.
• H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011.
• B. Dacorogna. Direct Methods in the Calculus of Variations, Springer, 1989.

Exam

The exam is oral. Here is a list of relevant theorems from the course:

• Direct Method (abstract)
• Sufficiency of convexity for lower semicontinuity
• Necessity of quasiconvexity for lower semicontinuity and Riemann-Lebesgue Lemma
• Application of the Direct Method to a class of convex and coercive functionals
• Quasiconvexity implies rank-one convexity
• Euler-Lagrange equation
• Fundamental Theorem of Gamma-convergence
• Liminf for one-dimensional Modica-Mortola
• Mountain-pass lemma in finite dimensions

For master students: you choose a theorem from the list and we then pick another one. You should be able to state these two correctly and comment on their proof. In addition, you should be aware of all other results presented in class

For PhD students: we pick a theorem from the list and you state it and prove it. In addition, you should be aware of all other results presented in class. Moreover, you report on one of these paper (your choice)

• paper 1
• paper 2
• paper 3
• paper 4
• paper 5
• paper 6
• paper 7
• paper 8
• paper 9
• paper 10
• paper 11
• paper 12