Γ -convergence and μ -capacities

Gianni Dal Maso

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)

  • Volume: 14, Issue: 3, page 423-464
  • ISSN: 0391-173X

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Dal Maso, Gianni. "$\Gamma $-convergence and $\mu $-capacities." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.3 (1987): 423-464. <http://eudml.org/doc/84013>.

@article{DalMaso1987,
author = {Dal Maso, Gianni},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {relaxed problems; Choquet capacity; -convergence},
language = {eng},
number = {3},
pages = {423-464},
publisher = {Scuola normale superiore},
title = {$\Gamma $-convergence and $\mu $-capacities},
url = {http://eudml.org/doc/84013},
volume = {14},
year = {1987},
}

TY - JOUR
AU - Dal Maso, Gianni
TI - $\Gamma $-convergence and $\mu $-capacities
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 3
SP - 423
EP - 464
LA - eng
KW - relaxed problems; Choquet capacity; -convergence
UR - http://eudml.org/doc/84013
ER -

References

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  1. [1] H. Attouch: Variational convergence for functions and operators. Pitman, London, 1984. Zbl0561.49012MR773850
  2. [2] J.R. Baxter, N.C. Jain: Asymptotic capacities for finely divided bodies and stopped diffusions. Illinois J. Math.31 (1987), 469-495. Zbl0618.60072MR892182
  3. [3] J.R. Baxter, G. Dal Maso, U.Mosco: Stopping times and Γ-convergence. Trans. Amer. Math. Soc.303 (1987), 1-38. Zbl0627.60071
  4. [4] M. Brelot: On Topologies and Boundaries in Potential Theory. Lecture Notes in Mathematics175, Springer, Berlin, 1971. Zbl0222.31014MR281940
  5. [5] G. Buttazzo, G. Dal Maso, U.Mosco: A derivation theorem for capacities with respect to a Radon measure. J. Funct. Anal.71 (1987), 263-278. Zbl0622.28006MR880980
  6. [6] G. Choquet: Forme abstraite du théorème de capacitabilité. Ann. Inst. Fourier9 (1959), 83-89. Zbl0093.29701MR112844
  7. [7] G. Dal Maso: Convergence faible et capacités. Boll. Un. Mat. Ital. 17 - B (1980), 440-457. Zbl0518.28001MR580533
  8. [8] G. Dal Maso: Asymptotic behaviour of minimum problems with bilateral obstacles. Ann. Mat. Pura Appl.129 (1981), 327-366. MR648338
  9. [9] G. Dal Maso: On the integral representation of certain local functionals. Ricerche Mat.32 (1983), 85-113. Zbl0543.49001MR740203
  10. [10] G. Dal Maso: Some necessary and sufficient conditions for the convergence of sequences of unilateral convex sets. J. Funct. Anal.62 (1985), 119-159. Zbl0582.49008MR791845
  11. [11] G. Dal Maso, U.Mosco: Wiener's criterion and Γ-convergence. Appl. Math Optim.15 (1987), 15-63. Zbl0644.35033
  12. [12] G. Dal Maso, U.Mosco: The Wiener modulus of a radial measure. To appear on Houston J. Math. Zbl0696.31009MR1002080
  13. [13] G. Dal Maso, U. Mosco: Wiener criteria and energy decay for relaxed Dirichlet problems. Arch. Rational Mech. Anal.95 (1986), 345-387. Zbl0634.35033MR853783
  14. [14] E. De Giorgi, G. Dal Maso: Γ-convergence and calculus of variations. In J.P. Cecconi, T. Zolezzi (eds) Mathematical Theories of Optimization. Proceedings, S. Margherita Ligure, 1981. Lecture Notes in Mathematics979, Springer, Berlin, 1983. Zbl0511.49007
  15. [15] E. De Giorgi, T. Franzoni: Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Sci. Fis. Natur.58 (1975), 842-850; Rend. Sem. Mat. Brescia3 (1979), 63-101. Zbl0339.49005MR448194
  16. [16] E. De Giorgi, G. Letta: Une notion générale de convergence faible pour des fonctions croissantes d' ensemble. Ann. Scuola Norm. Sup. Pisa Cl. Sci.4 (1977), 61-99. Zbl0405.28008MR466479
  17. [17] J.L. Doob: Classical potential theory and its probabilistic counterpart. Springer, Berlin, 1984. Zbl0549.31001MR731258
  18. [18] H. Federer, W.P. Ziemer: The Lebesgue set of function whose distribution derivatives are p-th power summable. Indiana Univ. Math. J.22 (1972), 139-158. Zbl0238.28015MR435361
  19. [19] B. Fuglede: The quasi topology associated with a countably subadditive set function. Ann. Inst. Fourier21 (1971), 123-169. Zbl0197.19401MR283158
  20. [20] B. Fuglede: Finely harmonic functions. Lecture notes in Mathematics289, Springer, Berlin. 1972. Zbl0248.31010MR450590
  21. [21] U. Mosco: Convergence of convex sets and of solutions of variational inequalities. Adv. in Math.3 (1969), 510-585. Zbl0192.49101MR298508
  22. [22] G. Stampacchia: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier15 (1965), 189-258. Zbl0151.15401MR192177

Citations in EuDML Documents

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  1. Nicolas Varchon, Optimal measures for the fundamental gap of Schrödinger operators
  2. Carlos Conca, François Murat, Claudia Timofte, A generalized strange term in Signorini’s type problems
  3. Michele Balzano, Lino Notarantonio, On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
  4. Gianni Dal Maso, François Murat, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators
  5. Carlos Conca, François Murat, Claudia Timofte, A Generalized Strange Term in Signorini's Type Problems
  6. Gianni Dal Maso, François Murat, Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains
  7. Enrico Vitali, Convergence of unilateral convex sets in higher order Sobolev spaces

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