1. Integral representation of unbounded variational functionals on Sobolev spaces
- Author
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Omar Anza Hafsa, Jean-Philippe Mandallena, Mathématiques, Informatique, Physique, et Applications / Université de Nîmes (MIPA), and Université de Nîmes (UNIMES)
- Subjects
Pure mathematics ,Integral representation ,Applied Mathematics ,General Mathematics ,Numerical analysis ,010102 general mathematics ,Dimension (graph theory) ,[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA] ,01 natural sciences ,Homogenization (chemistry) ,Sobolev space ,Nonlinear system ,0103 physical sciences ,Convergence (routing) ,010307 mathematical physics ,Relaxation (approximation) ,0101 mathematics ,[MATH]Mathematics [math] ,Mathematics - Abstract
In this paper we establish an unbounded version of the integral representation theorem by Buttazzo and Dal Maso [see Buttazzo Dal Maso (Nonlinear Anal 9(6):515–532, 1985) and also Bouchitte et al. (Arch Ration Mech Anal 165(3), 187–242, 2002)]. More precisely, we prove an integral representation theorem (with a formula for the integrand) for functionals defined on $$W^{1,p}$$ with $$p>N$$ (N being the dimension) that do not satisfy a standard p-growth condition from above and can take infinite values. Applications to $$\Gamma $$ -convergence, relaxation and homogenization are also developed. more...
- Published
- 2021