Arkiv för Matematik

  • Ark. Mat.
  • Volume 41, Number 1 (2003), 95-104.

Continuity of weak solutions of elliptic partial differential equations

Visa Latvala

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Abstract

The continuity of weak solutions of elliptic partial differential equations $div \mathcal{A}(x,\nabla u) = 0$ is considered under minimal structure assumptions. The main result guarantees the continuity at the point x0 for weakly monotone weak solutions if the structure of A is controlled in a sequence of annuli $B(x_0 ,R_j )\backslash \bar B(x_0 ,r_j )$ with uniformly bounded ratio Rj/rj such that limj→∞Rj=0. As a consequence, we obtain a sufficient condition for the continuity of mappings of finite distortion.

Article information

Source
Ark. Mat., Volume 41, Number 1 (2003), 95-104.

Dates
Received: 27 August 2001
Revised: 8 March 2002
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898793

Digital Object Identifier
doi:10.1007/BF02384569

Mathematical Reviews number (MathSciNet)
MR1971942

Zentralblatt MATH identifier
1035.35021

Rights
2003 © Institut Mittag-Leffler

Citation

Latvala, Visa. Continuity of weak solutions of elliptic partial differential equations. Ark. Mat. 41 (2003), no. 1, 95--104. doi:10.1007/BF02384569. https://projecteuclid.org/euclid.afm/1485898793


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