Explore gamma convergence in this comprehensive lecture from the International Centre for Theoretical Sciences' program on Multi-Scale Analysis and Theory of Homogenization. Delve into minimization problems, coercivity, and lower semi-continuity concepts. Examine integral functions, weak lower semi-continuity, and their applications in homogenization theory. Work through exercises and problem-solving sessions to reinforce understanding of these advanced mathematical concepts. Gain insights into recent developments and ongoing research in multi-scale analysis, preparing you for further study or collaboration in this field.
Overview
Syllabus
Gamma Convergence Lecture 2
Minimization problem
Alpha = inf Fy [Minimal value; Minimal point; Minimal sequence]
Graphs
Coercine
Definition
Theorem: Assume F. X-is Coercine and lsc
Proof:
F is given by an integral functions
Problem Solution
Concept of derivative
Exercise: assume u E C2 Omega
Integral functions
Proposition: F is lsc in strong topology
Two other functions
Weak lower semi continuity
Homogenization
Next
Taught by
International Centre for Theoretical Sciences
