The Passage From Discrete Systems to Continuous Variational Problems
Andrea Braides
These notes contain material related to the five lectures that I have delivered at the University of Utah in the week 16--20 May 2005. They are organized in the order of the lectures; namely,
1. Spin systems. An introduction to lattice systems
2. Limits of finite-difference lattice systems.
3. Bounds for linear networks.
4. A model for a membrane with randomly-distributed defects.
5. Derivation of fracture energies from
inter-atomic potentials.
The notes are thought just as a complement and reference
for the single lectures, and not as a whole: I must warn that the chapters
are unevenly written. Some are elaboration of articles that have already
appeared and some have been completely written for the occasion. As a consequence
some notation may slightly vary from chapter to chapter.
Related links:
Gamma-convergence
for beginners - notes of a PhD course
Course
on limits of one-dimensional discrete systems
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