The second Stekloff eigenvalue and energy dissipation inequalities for functionals with surface energy

SIAM Journal on Mathematical Analysis

Volumn 29, Issue 3, 1998, Pages 673-680

  Lipton, Robert ^a  

^a Worcester Polytechnic Institute   (United States)

Author keywords

Heat conduction; Isoperimetric inequalities; Size effects; Stekloff eigenvalue

Indexed keywords

EID: 0032391140     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141096310144     Document Type: Article

References (19)

1. G. ALESSANDRINI AND R. MAGNANINI, Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions, SIAM J. Math. Anal., 25 (1994). pp. 1259-1208.
2. J. H. BRAMBLE AND L. E. PAYNE, Bounds in the Neumann problem for second order uniformly elliptic operators, Pacific J. Math., 12 (1962), pp. 823-833.
3. D. CHENAIS, On the existence of a solution in a domain identification problem, J. Math. Anal. Appl., 52 (1975), pp. 189-219.
4. D. CHENAIS, Homéomorphisme entre ouverts lipschitziens, Ann. Mat. Pura Appl., 118 (1980), pp. 343-398.
5. Y. C. CHIEW AND E. D. GLANDT, Effective conductivity of dispersions: The effect of resistance at particle interfaces, Chem. Engrg. Sci., 42 (1987), pp. 2677-2685.
6. L. C. DAVIS AND B. E. ARTS, Thermal conductivity of metal-matrix composites, J. Appl. Phys., 77 (1995), pp. 4954-4960.
7. A. G. EVERY, Y. Tzou, D. P. H. HASSELMAN, AND R. RAJ, The effect of particle size on the thermal conductivity of ZnS/diamond composites, Acta Metall. Matter, 40 (1992), pp. 123-129.
8. D. P. H. HASSELMAN AND L. F. JOHNSON, Effective thermal conductivity of composites with interfacial thermal barrier resistance, J. Composite Materials, 21 (1987), pp. 508-515.
9. J. R. KUTTLER AND V. G. SIGILLITO, Inequalities for membrane, and Stekloff eigenvalues, J. Math. Anal. Appl., 23 (1968), pp. 148-160.
10. R. LIPTON, Energy minimizing configurations for mixtures of two imperfectly bonded conductors, J. Control Cybernet., to appear.
11. R. LIPTON AND B. VERNESCU, Composites with imperfect interface, Proc. Roy. Soc. London Ser. A, 452 (1996), pp. 329-358.
12. R. LIPTON AND B. VERNESCU, Critical radius, size effects, and inverse problems for composites with imperfect interface, J. Appl. Phys., 79 (1996), pp. 8964-8966.
13. K. A. LURIE AND A. V. CHERKAEV, Effective characteristics of composite materials and the optimal design of structural elemets, Uspekhi Mekaniki, Advances in Mechanics, 9 (1986), pp. 3-81; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R. Kohn, eds., Birkhäuser, Basel, 1997, pp. 175-258 (in English).
14. K. A. LURIE AND A. V. CHERKAEV, Effective characteristics of composite materials and the optimal design of structural elemets, Uspekhi Mekaniki, Advances in Mechanics, 9 (1986), pp. 3-81; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R. Kohn, eds., Birkhäuser, Basel, 1997, pp. 175-258 (in English).
15. F. MURAT AND L. TARTAR, Calcul des variations et homogénéisation, in Les Methodes de l'Homogénéisation: Théorie et Applications en Physique Coll. de la Dir. des Etudes et Recherches de Electr. del. France, Eyrolles, Paris, 1985, pp. 319-370; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R. Kohn, eds., Birkhäuser, Basel, 1997, pp. 139-174 (in English).
16. F. MURAT AND L. TARTAR, Calcul des variations et homogénéisation, in Les Methodes de l'Homogénéisation: Théorie et Applications en Physique Coll. de la Dir. des Etudes et Recherches de Electr. del. France, Eyrolles, Paris, 1985, pp. 319-370; in Topics in the Mathematical Modelling of Composite Materials, A. Cherkaev and R. Kohn, eds., Birkhäuser, Basel, 1997, pp. 139-174 (in English).
17. L. E. PAYNE, Some isoperimetric inequalities for harmonic functions, SIAM J. Math. Anal., 3 (1970), pp. 354-359.
18. L. E. PAYNE, Isoperimetric inequalities and their applications, SIAM Rev., 9 (1967), pp. 453-488.
19. A. V. STEKLOFF, Sur les problémes fondamentaux en physique mathématique, Ann. Sci. Ecole Norm. Sup., 19 (1902), pp. 455-490.