Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities-Reference-Cited by-同舟云学术

Relaxation of functionals with linear growth: Interactions of emerging measures and free discontinuities

Published:2022-01-06 Issue:0 Volume:0 Page:
ISSN:1864-8258
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Krömer Stefan¹^ORCID,Kružík Martin²^ORCID,Zappale Elvira³^ORCID

Affiliation:

1. Czech Academy of Sciences , Institute of Information Theory and Automation , Pod vodárenskou věží 4, CZ-182 08 Prague 8 , Czech Republic

2. Czech Academy of Sciences , Institute of Information Theory and Automation , Pod vodárenskou věží 4, CZ-182 08 Prague 8 ; and Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ–166 29 Prague 6 , Czech Republic

3. Dipartimento di Scienze di Base ed Applicate per l’Ingegneria , Sapienza - Università di Roma , Via Antonio Scarpa, 16 00161 , Roma , RM Italy

Abstract

Abstract For an integral functional defined on functions ( u , v ) ∈ W 1 , 1 × L 1

{(u,v)\in W^{1,1}\times L^{1}}

featuring a prototypical strong interaction term between u and v, we calculate its relaxation in the space of functions with bounded variations and Radon measures. Interplay between measures and discontinuities brings various additional difficulties, and concentration effects in recovery sequences play a major role for the relaxed functional even if the limit measures are absolutely continuous with respect to the Lebesgue one.

Funder

Istituto Nazionale di Alta Matematica “Francesco Severi”

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2021-0063/pdf

Reference30 articles.

1. E. Acerbi, G. Bouchitté and I. Fonseca, Relaxation of convex functionals: The gap problem, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 3, 359–390.

2. L. Ambrosio and G. Dal Maso, On the Relaxation in B ⁢ V ⁢ ( Ω ; ℝ m ) {BV(\Omega;\mathbb{R}^{m})} of quasi-convex integrals, J. Funct. Anal. 109 (1992), 76–97.

3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University, Oxford, 2000.

4. J.-F. Babadjian, E. Zappale and H. Zorgati, Dimensional reduction for energies with linear growth involving the bending moment, J. Math. Pures Appl. (9) 90 (2008), no. 6, 520–549.

5. M. Baía, S. Krömer and M. Kružík, Generalized W 1 , 1 {W^{1,1}} -Young measures and relaxation of problems with linear growth, SIAM J. Math. Anal. 50 (2018), no. 1, 1076–1119.

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