The Neumann problem for elliptic equations with nonsmooth coefficients: Part II

previous :: next

The Neumann problem for elliptic equations with nonsmooth coefficients: Part II

Carlos E. Kenig and Jill Pipher

Source: Duke Math. J. Volume 81, Number 1 (1995), 227-250.

First Page PDF: View first page of article (PDF, 118 KB)

Related Works:

See also: Carlos E. Kenig, Jill Pipher. The Neumann problem for elliptic equations with nonsmooth coefficients. Invent. Math. Vol. 113 (1983), pp. 447–509.

Mathematical Reviews (MathSciNet): MR1231834

Primary Subjects: 35J25

Secondary Subjects: 35B20, 35R05

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245467
Mathematical Reviews number (MathSciNet): MR1381976
Zentralblatt MATH identifier: 0854.35030
Digital Object Identifier: doi:10.1215/S0012-7094-95-08112-5

back to Table of Contents

References

[CFMS] L. Caffarelli, E. Fabes, S. Mortola, and S. Salsa, Boundary behavior of non-negative solutions of elliptic operators in divergence form, Indiana Univ. Math. J. 30 (1981), no. 4, 621–640.

Mathematical Reviews (MathSciNet): MR83c:35040

Zentralblatt MATH: 0512.35038

Digital Object Identifier: doi:10.1512/iumj.1981.30.30049

[Ch] I. Chavel, Eigenvalues in Riemannian Geometry, Pure Appl. Math., vol. 115, Academic Press, Orlando, Florida, 1984.

Mathematical Reviews (MathSciNet): MR86g:58140

Zentralblatt MATH: 0551.53001

[D] B. Dahlberg, On the absolute continuity of elliptic measures, Amer. J. Math. 108 (1986), no. 5, 1119–1138.

Mathematical Reviews (MathSciNet): MR88i:35061

Zentralblatt MATH: 0644.35032

Digital Object Identifier: doi:10.2307/2374598

JSTOR: links.jstor.org

[DK] B. E. J. Dahlberg and C. Kenig, Hardy spaces and the Neumann problem in $L^p$ for Laplace's equation in Lipschitz domains, Ann. of Math. (2) 125 (1987), no. 3, 437–465.

Mathematical Reviews (MathSciNet): MR88d:35044

Zentralblatt MATH: 0658.35027

Digital Object Identifier: doi:10.2307/1971407

JSTOR: links.jstor.org

[DJK] B. E. J. Dahlberg, D. Jerison, and C. Kenig, Area integral estimates for elliptic differential operators with nonsmooth coefficients, Ark. Mat. 22 (1984), no. 1, 97–108.

Mathematical Reviews (MathSciNet): MR85h:35021

Zentralblatt MATH: 0537.35025

Digital Object Identifier: doi:10.1007/BF02384374

[DeG] E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25–43.

Mathematical Reviews (MathSciNet): MR20:172

Zentralblatt MATH: 0084.31901

[Fe1] R. Fefferman, A criterion for the absolute continuity of the harmonic measure associated with an elliptic operator, J. Amer. Math. Soc. 2 (1989), no. 1, 127–135.

Mathematical Reviews (MathSciNet): MR90b:35068

Zentralblatt MATH: 0694.35050

Digital Object Identifier: doi:10.2307/1990914

JSTOR: links.jstor.org

[FJL1] E. Fabes, M. Jodeit, and J. Lewis, On the spectra of a Hardy kernel, J. Funct. Anal. 21 (1976), no. 2, 187–194.

Mathematical Reviews (MathSciNet): MR52:15114

Zentralblatt MATH: 0321.47038

Digital Object Identifier: doi:10.1016/0022-1236(76)90076-8

[FJL2] E. Fabes, M. Jodeit, and J. Lewis, Double layer potentials for domains with corners and edges, Indiana Univ. Math. J. 26 (1977), no. 1, 95–114.

Mathematical Reviews (MathSciNet): MR55:5879

Zentralblatt MATH: 0363.35010

Digital Object Identifier: doi:10.1512/iumj.1977.26.26007

[FKP] R. A. Fefferman, C. E. Kenig, and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. (2) 134 (1991), no. 1, 65–124.

Mathematical Reviews (MathSciNet): MR93h:31010

Zentralblatt MATH: 0770.35014

Digital Object Identifier: doi:10.2307/2944333

JSTOR: links.jstor.org

[K] C. Kenig, Harmonic analysis techniques for second order elliptic boundary value problems, CBMS Regional Conference Series in Mathematics, vol. 83, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1994.

Mathematical Reviews (MathSciNet): MR96a:35040

Zentralblatt MATH: 0812.35001

[KP] C. Kenig and J. Pipher, The Neumann problem for elliptic equations with non-smooth coefficients, Invent. Math. 113 (1993), no. 3, 447–509.

Mathematical Reviews (MathSciNet): MR95b:35046

Zentralblatt MATH: 0807.35030

Digital Object Identifier: doi:10.1007/BF01244315

[Ko] V. Kondratev, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obšč. 16 (1967), 209–292.

Mathematical Reviews (MathSciNet): MR37:1777

[Me] N. Meyers, An $L^p$ estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci (3) 17 (1963), 189–206.

Mathematical Reviews (MathSciNet): MR28:2328

Zentralblatt MATH: 0127.31904

[Mo] J. Moser, On Harnack's theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577–591.

Mathematical Reviews (MathSciNet): MR28:2356

Zentralblatt MATH: 0111.09302

Digital Object Identifier: doi:10.1002/cpa.3160140329

[PrW] M. Protter and H. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, N.J., 1967.

Mathematical Reviews (MathSciNet): MR36:2935

Zentralblatt MATH: 0549.35002

[V] G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), no. 3, 572–611.

Mathematical Reviews (MathSciNet): MR86e:35038

Zentralblatt MATH: 0589.31005

Digital Object Identifier: doi:10.1016/0022-1236(84)90066-1

previous :: next