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Estimates for the electric field in the presence of adjacent perfectly conducting spheres
Author(s):
Habib
Ammari;
George
Dassios;
Hyeonbae
Kang;
Mikyoung
Lim
Journal:
Quart. Appl. Math.
65
(2007),
339-355.
MSC (2000):
Primary 35J25;
Secondary 73C40
Posted:
January 16, 2007
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Abstract:
In this paper we prove that, unlike the two-dimensional case, the electric field in the presence of closely adjacent spherical perfect conductors does not blow up even though the separation distance between the conducting inclusions approaches zero.
References:
-
- 1.
- H. Ammari, H. Kang, and M. Lim, Gradient estimates for solutions to the conductivity problem, Math. Ann., 332 (2005), 277-286. MR 2178063 (2006h:78010)
- 2.
- H. Ammari, H. Kang, H. Lee, J. Lee, and M. Lim, Optimal bounds on the gradient of solutions to conductivity problems, preprint.
- 3.
- I. Babuska, B. Andersson, P. Smith, and K. Levin, Damage analysis of fiber composites. I. Statistical analysis on fiber scale, Comput. Methods Appl. Mech. Engrg., 172 (1999), 27-77. MR 1685902 (2000a:74115)
- 4.
- E. Bonnetier and M. Vogelius, An elliptic regurality result for a composite medium with touching fibers of circular cross-section, SIAM J. Math. Anal., 31 (2000), 651-677. MR 1745481 (2002a:35052)
- 5.
- B. Budiansky and G.F. Carrier, High shear stresses in stiff fiber composites, J. Appl. Mech., 51 (1984), 733-735.
- 6.
- A. Charalambopoulos, G. Dassios, and M. Hadjinicolaou, An analytic solution for low-frequency scattering by two soft spheres, SIAM J. Appl. Math., 58 (1998), 370-386. MR 1617658 (98m:35020)
- 7.
- J.B. Keller, Stresses in narrow regions, Trans. ASME J. Appl. Mech., 60 (1993), 1054-1056.
- 8.
- J.B. Keller, Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders, J. Appl. Phys., 3 (1963), 991-993.
- 9.
- Y.Y. Li and L. Nirenberg, Estimates for elliptic systems from composite material, Comm. Pure Appl. Math., LVI (2003), 892-925. MR 1990481 (2004k:35097)
- 10.
- Y.Y. Li and M. Vogelius, Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients, Arch. Rational Mech. Anal., 153 (2000), 91-151. MR 1770682 (2001m:35083)
- 11.
- X. Markenscoff, Stress amplification in vanishing small geometries, Comput. Mech., 19 (1996), 77-83.
- 12.
- P. Moon and D.E. Spencer, Field Theory Handbook, 2nd Ed. Springer-Verlag, Berlin, 1988. MR 947546 (89i:00026)
- 13.
- H. Yun, Estimates for electric fields blown up between closely adjacent conductors with arbitrary shape, preprint, 2006.
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Additional Information:
Habib
Ammari
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email:
ammari@cmapx.polytechnique.fr
George
Dassios
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, United Kingdom
Email:
G.Dassios@damtp.cam.ac.uk
Hyeonbae
Kang
Affiliation:
Department of Mathematical Sciences and RIM, Seoul National University, Seoul 151-747, Korea
Email:
hkang@math.snu.ac.kr
Mikyoung
Lim
Affiliation:
Centre de Mathématiques Appliquées, CNRS UMR 7641 and Ecole Polytechnique, 91128 Palaiseau Cedex, France
Email:
mklim@cmapx.polytechnique.fr
PII:
S0033-569X-07-01034-1
Keywords:
Electric field,
gradient estimates,
composite materials
Received by editor(s):
April 30, 2006
Posted:
January 16, 2007
Copyright of article:
Copyright
2007,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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