2 INTEGRAL PROBLEMS
- Gamma-Convergence for Beginners
- Oxford University Press
This chapter deals with integral problems. Using examples, it illustrates the need to use weak topologies to obtain compactness and coerciveness conditions. The sufficiency and necessity of the convexity of integrands is proved. A characterization of Gamma-convergence in terms of convex analysis is given. The result is extended to Sobolev spaces, where the problem of dealing with boundary values is introduced. Examples of degenerate integrals with limits defined on discontinuous functions or by functions of the sup-norm are given.
integral functionals, weak topologies, Sobolev spaces, Convex Analysis, boundary value problems, degenerate integral functionals
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