On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
Rendiconti del Seminario Matematico della Università di Padova, Tome 100 (1998), pp. 249-282. 
@article{RSMUP_1998__100__249_0,
     author = {Balzano, Michele and Notarantonio, Lino},
     title = {On the asymptotic behavior of {Dirichlet} problems in a riemannian manifold less small random holes},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {249--282},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {100},
     year = {1998},
     mrnumber = {1675287},
     zbl = {0922.31008},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1998__100__249_0/}
}
TY  - JOUR
AU  - Balzano, Michele
AU  - Notarantonio, Lino
TI  - On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 1998
SP  - 249
EP  - 282
VL  - 100
PB  - Seminario Matematico of the University of Padua
UR  - http://www.numdam.org/item/RSMUP_1998__100__249_0/
LA  - en
ID  - RSMUP_1998__100__249_0
ER  - 
%0 Journal Article
%A Balzano, Michele
%A Notarantonio, Lino
%T On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
%J Rendiconti del Seminario Matematico della Università di Padova
%D 1998
%P 249-282
%V 100
%I Seminario Matematico of the University of Padua
%U http://www.numdam.org/item/RSMUP_1998__100__249_0/
%G en
%F RSMUP_1998__100__249_0
Balzano, Michele; Notarantonio, Lino. On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes. Rendiconti del Seminario Matematico della Università di Padova, Tome 100 (1998), pp. 249-282. http://www.numdam.org/item/RSMUP_1998__100__249_0/

[1] T. Aubin, Nonlinear Analysis on Manifold, Monge-Ampére Equations, Grundlehren der Matematischen Wiessenschaften, Springer-Verlag, New York, Berlin, Tokio (1982). | MR | Zbl

[2] M. Balzano, Randon relaxed dirichlet problems, Ann. Mat. Pura Appl., 53 (1988), pp. 133-174. | MR | Zbl

[3] P. Bérard - S. Gallot, Remarques sur quelques estimées géometriques explicites, C. R. Acad. Sci. Paris, 297 (1983), pp. 185-188. | MR | Zbl

[4] G. Besson, Comportement asymptotique des valeurs propres du Laplacien dans un trou, Bull. Soc. Math. France, 113 (1985), pp. 211-230. | Numdam | MR | Zbl

[5] R. Bishop - R. CRITTENDEN, Geometry of Manifolds, Academic Press, New York, London (1964). | MR | Zbl

[6] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, New York (1984). | MR | Zbl

[7] I. Chavel - E. FELDMAN, Spectra of domains in compact manifolds, J. Funct. Anal., 30 (1978), pp. 198-222. | MR | Zbl

[8] I. Chavel - E. FELDMAN, The Lenz shift and Wiener sausage in Riemannian manifolds, Compositio Math., 60 (1986), pp. 65-84. | Numdam | MR | Zbl

[9] I. Chavel - E. Feldman, Spectra of manifolds less a small domain, Duke Math., J., 56 (1988), pp. 399-414. | MR | Zbl

[10] G. Courtois, Comportement du spectre d'une variété riemanniene compacte sous perturbation topologique par excision d'une domaine, Ph.D. thesis, Inst. Fourier (1987).

[11] G. Dal Maso, γ-convergence and μ-capacities, Ann. Scuola Norm. Sup. Cl. Sci. (4) (1987), pp. 432-464. | Numdam | Zbl

[12] G., Dal Maso An Introduction to Γ-convergence, Birkhäuser (1993). | Zbl

[13] G. Dal Maso - R. Gulliver - U. Mosco, Asymptotic spectrum of manifolds of increasing topological type, to appear.

[14] G. Dal Maso - U. Mosco, Wiener criterion and Γ-convergence, Appl. Math. Opt., 15 (1987), pp. 15-63. | Zbl

[15] E. Hruslov, The method of orthogonal projection and the Dirichlet problem in domains with a fine-grained boundary, Math. U.S.S.R. Sb. (1972). | Zbl

[16] E. Hruslov, The first boundary problem in domains with a complicated boundary for higher order equation, Math. U.S.S.R. Sb., 32 (1977), pp. 535-549. | Zbl

[17] M. Kac, Probabilistic method in some problems of scattering theory, Rocky Mountain J. Math., 4 (1974), pp. 511-537. | MR | Zbl

[18] D. Kinderlehrer - G. STAMPACCHIA, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York (1980). | MR | Zbl

[19] W. Littman - G. Stampacchia - H. Weinberger, Regular points for elliptic equation with discontinuous coefficients, Ann. Scuola Norm. Pisa Cl. Sci., 17 (1963), pp. 45-79. | Numdam | MR | Zbl

[20] L. Notarantonio, Asymptotic behavior of Dirichlet problems on a Riemannian manifold, Ricerche di Mat., 41 (1992), pp. 327-367. | MR | Zbl

[21] J. Rauch - M. Taylor, Potential scattering theory on wildly perturbed domains, J. Funct. Anal., 18 (1975), pp. 27-59. | MR | Zbl

[22] W. Ziemer, Weakly Differentiable Functions, Springer-Verlag, Berlin, Heidelberg, New York (1989). | MR | Zbl