Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T23:48:44.719Z Has data issue: false hasContentIssue false
  • English
  • Français

HÖLDER ESTIMATES FOR LINEAR SECOND-ORDER EQUATIONS

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  17 November 2010

C. G. Böhmer
C. G. Böhmer*
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, U.K. (email: c.boehmer@ucl.ac.uk)
Get access

Abstract

We consider uniformly elliptic, second-order, linear partial differential equations depending on three variables in bounded domains. We obtain interior Hölder estimates for the first derivatives of the bounded solutions independent of the regularity assumptions of the differential operator.

MSC classification

Secondary: 35J15: Second-order elliptic equations 35B45: A priori estimates
Type
Research Article
Information
Mathematika , Volume 57 , Issue 2 , July 2011 , pp. 315 - 327
Copyright
Copyright © University College London 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Cordes, H. O., Über die erste Randwertaufgabe bei quasilinearen differentialgleichungen zweiter ordnung in mehr als zwei variablen. Math. Ann. 131 (1956), 278.CrossRefGoogle Scholar
[2]Gilbarg, D. and Trudinger, N. S., Elliptic Partial Differential Equations of Second Order, Springer (Berlin, 1977).CrossRefGoogle Scholar
[3]Krylov, N. V., Lectures on Elliptic and Parabolic Equations in Hölder Spaces (Graduate Studies in Mathematics 12), American Mathematical Society (Providence, RI, 1996).CrossRefGoogle Scholar
[4]Ladyženskaja, O. A. and Ural’ceva, N. N., Quasilinear elliptic equations and variational problems in several independent variables. Uspekhi Mat. Nauk 16 (1961), 19 (in Russian).Google Scholar
[5]Morrey, C. B. Jr, On the solutions of quasilinear elliptic partial differential equations. Trans. Amer. Math. Soc. 43 (1938), 126.CrossRefGoogle Scholar
[6]Morrey, C. B. Jr, Second order elliptic equations in several variables and Hölder continuity. Math. Z. 72 (1959), 146.CrossRefGoogle Scholar
[7]Morrey, C. B. Jr, Multiple Integrals in the Calculus of Variations, Springer (Berlin, 1966).CrossRefGoogle Scholar
[8]Nirenberg, L., On nonlinear elliptic partial differential equations and Hölder continuity. Commun. Pure Appl. Math. 6 (1953), 103.CrossRefGoogle Scholar
[9]Safonov, M. V., Unimprovability of estimates of Hölder constants for solutions of linear elliptic equations with measurable coefficients. Math. USSR Sb. 60 (1988), 269.CrossRefGoogle Scholar