Asymptotic Behaviour of a Thin Insulation Problem

Pierpaolo Esposito; Giuseppe Riey

doi:10.68381/jca1022

Abstract

We consider a problem of thermal insulation and we study, by means of

\Gamma

-convergence, the best way to put the insulator when its mass tends to zero.

Author information

Contact details are reproduced from the original publication and may be historical.

Pierpaolo Esposito

Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, Roma 00133,
Italy

Giuseppe Riey

Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, Roma 00133,
Italy

Keywords

Γ-convergence
thermal insulation
asymptotic behaviour

Mathematics Subject Classification

35B40, 35J05, 35B37

References

E. Acerbi, G. Buttazzo: Reinforcement problems in the calculus of variations, Ann. Inst. H. Poincaré - Analyse Non Linéaire 3(4) (1986) 273–284.https://doi.org/10.1016/s0294-1449(16)30380-8 Google Scholar
L. Ambrosio, N. Fusco, D. Pallara: Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford (2000).https://doi.org/10.1093/oso/9780198502456.001.0001 Google Scholar
M. Boutkrida, J. Mossino, G. Moussa: On the torsional rigidity problem with nonhomogenous reinforcement, Papers in memory of Ennio De Giorgi, Ricerche Mat. 48, suppl. (1999) 1–24.Google Scholar
M. Boutkrida, J. Mossino, G. Moussa: On nonhomogenous reinforcements of varying shape and different exponents, Boll. U.M.I. Sez. B Artic. Ric. Mat. (8) 2(3) (1999) 517–536.Google Scholar
H. Brezis: Analyse Fonctionelle - Théorie et Applications, Masson, Paris (1983).Google Scholar
H. Brezis, L. A. Caffarelli, A. Friedman: Reinforcement problems for elliptic equations and variational inequalities, Ann. Mat. Pura Appl. 123(4) (1980) 219–246.https://doi.org/10.1007/BF01796546 Google Scholar
G. Buttazzo: An optimization problem for thin insulating layers around a conducting medium, in: Boundary Control and Boundary Variations (Nice, 1986), Lecture Notes in Comput. Sci. 100, Springer (1988) 91–95.https://doi.org/10.1007/BFb0041912 Google Scholar
G. Buttazzo: Thin insulating layers: The optimization point of view, in: Proceedings of "Material Instabilities in Continuum Mechanics and Related Mathematical Problems", Edinburgh 1985-1986, Oxford University Press, Oxford (1988) 11-19.Google Scholar
G. Dal Maso: An Introduction to Γ-Convergence, Birkhäuser, Boston (1993).https://doi.org/10.1007/978-1-4612-0327-8 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.

[1] E. Acerbi, G. Buttazzo: Reinforcement problems in the calculus of variations, Ann. Inst. H. Poincaré - Analyse Non Linéaire 3(4) (1986) 273–284.https://doi.org/10.1016/s0294-1449(16)30380-8 Google Scholar

[2] L. Ambrosio, N. Fusco, D. Pallara: Functions of Bounded Variation and Free Discontinuity Problems, Clarendon Press, Oxford (2000).https://doi.org/10.1093/oso/9780198502456.001.0001 Google Scholar

[3] M. Boutkrida, J. Mossino, G. Moussa: On the torsional rigidity problem with nonhomogenous reinforcement, Papers in memory of Ennio De Giorgi, Ricerche Mat. 48, suppl. (1999) 1–24.Google Scholar

[4] M. Boutkrida, J. Mossino, G. Moussa: On nonhomogenous reinforcements of varying shape and different exponents, Boll. U.M.I. Sez. B Artic. Ric. Mat. (8) 2(3) (1999) 517–536.Google Scholar

[5] H. Brezis: Analyse Fonctionelle - Théorie et Applications, Masson, Paris (1983).Google Scholar

[6] H. Brezis, L. A. Caffarelli, A. Friedman: Reinforcement problems for elliptic equations and variational inequalities, Ann. Mat. Pura Appl. 123(4) (1980) 219–246.https://doi.org/10.1007/BF01796546 Google Scholar

[7] G. Buttazzo: An optimization problem for thin insulating layers around a conducting medium, in: Boundary Control and Boundary Variations (Nice, 1986), Lecture Notes in Comput. Sci. 100, Springer (1988) 91–95.https://doi.org/10.1007/BFb0041912 Google Scholar

[8] G. Buttazzo: Thin insulating layers: The optimization point of view, in: Proceedings of "Material Instabilities in Continuum Mechanics and Related Mathematical Problems", Edinburgh 1985-1986, Oxford University Press, Oxford (1988) 11-19.Google Scholar

[9] G. Dal Maso: An Introduction to Γ-Convergence, Birkhäuser, Boston (1993).https://doi.org/10.1007/978-1-4612-0327-8 Google Scholar