International Journal of Differential Equations

On Carlson's Type Removability Test for the Degenerate Quasilinear Elliptic Equations

Farman I. Mamedov, Aslan D. Quliyev, and Mirfaig M. Mirheydarli

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Abstract

Carlson's type theorem on removable sets for α-Holder continuous solutions is investigated for the quasilinear elliptic equations divA(x,u,u)=0, having degeneration ω in the Muckenhoupt class. In partial, when α is sufficiently small and the operator is weighted p-Laplacian, we show that the compact set E is removable if and only if the Hausdorff measure Λωp+(p1)α(E)=0.

Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 198606, 23 pages.

Dates
Received: 27 May 2011
Accepted: 13 August 2011
First available in Project Euclid: 25 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485313253

Digital Object Identifier
doi:10.1155/2011/198606

Mathematical Reviews number (MathSciNet)
MR2847602

Zentralblatt MATH identifier
1237.35075

Citation

Mamedov, Farman I.; Quliyev, Aslan D.; Mirheydarli, Mirfaig M. On Carlson's Type Removability Test for the Degenerate Quasilinear Elliptic Equations. Int. J. Differ. Equ. 2011 (2011), Article ID 198606, 23 pages. doi:10.1155/2011/198606. https://projecteuclid.org/euclid.ijde/1485313253


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