Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients

Archive for Rational Mechanics and Analysis

Volumn 153, Issue 2, 2000, Pages 91-151

  Li, Yan Yan ^a   Vogelius, Michael ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034413375     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050000082     Document Type: Article

References (10)

1. S. AGMON, A. DOUGLIS & L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Comm. Pure Appl. Math. 17 (1964), pp. 35-92.
2. I. BABUSKA, B. ANDERSSON, P.J. SMITH & K. LEVIN, Damage analysis of fiber composites. Part I: statistical analysis on fiber scale. The Aeronautical Research Institute of Sweden, Technical Note # 15, 1998.
3. E. BONNETIER & M. VOGELIUS, An elliptic regularity result for a composite medium with "touching" fibers of circular cross-section. SIAM J. Math. Anal. 31 (2000), pp. 651-677.
4. B. BUDIANSKY & G.F. CARRIER, High shear stresses in stiff fiber composites. J. App. Mech. 51 (1984), pp. 733-735.
5. L. CAFFARELLI, Interior a priori estimates for solutions of fully nonlinear equations. Ann. of Math. 130 (1989), 189-213.
6. L. CAFFARELLI & X. CABRE, Fully Nonlinear Elliptic Equations, AMS Colloqium Publications 43, AMS, Providence, RI, 1995.
7. M. GIAQINTA, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies 105, Princeton University, N.J. 1983.
8. D. GILBARG & N.S. TRUDINGER, Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1983.
9. X. MARKENSCOFF, Stress amplification in vanishingly small geometries. Computational Mechanics 19 (1996), 77-83.
10. M. SCHECHTER, A generalization of the problem of transmission. Ann. Scuola Norm. Sup. Pisa 4 (1960), 207-236.