Multidimensional calculus of variations 1000-1M10WRW
The purpose of the lecture is to describe modern methods in the multidimensional calculus of variations, including direct methods in the calculus of variations, Young measure theory, elements of the theory of compensated compactness, methods of convex integration. The investigation background for these methods includes questions arising in elasticity theory, crystalography and mathematical methods in economics. The theory contains many open questions, starting with Morrey's conjecture of 1952 and up to many very recent open problems deriving from the development of experimental investigations in the theory of elastic crystals.
The lecture may interest those who are interested in mathematical models in physics/economy, as well as those students or PhD students who are looking for open questions in analysis in the broad sense.
Requirements: knowledge of Analysis II and Functional Analysis I. Knowledge of PDEs is welcome but not necessary.
Type of course
Course coordinators
Bibliography
B. Dacorogna, Direct Methods in the Calculus of Variations, Springer Berlin, 1989
S. Muller, Variational Models for Microstructure and Phase Transitions, Lecture Notes in Mathematics, Springer, 1999
P. Pedregal, Parametrized Measures and Variational Principles, Birkhauser Basel, 1997
J. M. Ball: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1978), 337--403.
Additional information
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