An elliptic regularity result for a composite medium with "touching" fibers of circular cross-section

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 3, 2000, Pages 651-677

  Bonnetier, Eric ^a   Vogelius, Michael ^b  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Composite materials; Elliptic regularity

Indexed keywords

EID: 0034376968     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098333980     Document Type: Article

References (10)

1. B. ANDERSSON, private communication, Aeronautical Research Institute of Sweden, 1998.
2. B. BUDIANSKY AND G. F. CARRIER, High shear stresses in stiff fiber composites, Trans. ASME J. Appl. Mech., 51 (1984), pp. 733-735.
3. E. DEGIORGI, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur., 3 (1957), pp. 25-43.
4. D. GILBARG AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order; Grundlehren Math. Wiss. 224, Springer-Verlag, Berlin, 1983.
5. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Boston, 1985.
6. J. B. KELLER, Stresses in narrow regions, Trans. ASME J. Appl. Mech., 60 (1993), pp. 1054-1056.
7. V. A. KOZLOV, V. G. MAZ'YA, AND J. ROSSMANN, Elliptic Boundary Value Problems in Domains with Point Singularities, Math. Surveys Monogr. 52, AMS, Providence, RI, 1989.
8. Y.-Y. LI AND M. VOGELIUS, Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients, Arch. Rational Mech. Anal., to appear.
9. X. MARKENSCOFF, Stress amplification in vanishingly small geometries, Comput. Mech., 19 (1996), pp. 77-83.
10. J. NASH, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math., 80 (1958), pp. 931-954.