论文信息 - Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients

Gradient Estimates for Solutions to Divergence Form Elliptic Equations with Discontinuous Coefficients

Abstract:In this paper we derive global W1,∞ and piecewise C1,α estimates for solutions to divergence form elliptic equations with piecewise Hölder continuous coefficients. The novelty of these estimates is that, even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients, they are independent of the distance between these surfaces.

M. Vogelius | Yanyan Li

[1] S. Agmon,et al. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .

[2] M. Schechter. A generalization of the problem of transmission , 1960 .

[3] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[4] Mariano Giaquinta,et al. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 , 1984 .

[5] George F. Carrier,et al. High Shear Stresses in Stiff-Fiber Composites , 1984 .

[6] L. Caffarelli. Interior a priori estimates for solutions of fully non-linear equations , 1989 .

[7] L. Caffarelli,et al. Fully Nonlinear Elliptic Equations , 1995 .

[8] Xanthippi Markenscoff,et al. Stress amplification in vanishingly small geometries , 1996 .

[9] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .

[10] Ivo Babuška,et al. Damage analysis of fiber composites Part I: Statistical analysis on fiber scale , 1999 .

[11] Eric Bonnetier,et al. An Elliptic Regularity Result for a Composite Medium with "Touching" Fibers of Circular Cross-Section , 2000, SIAM J. Math. Anal..