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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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.

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

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

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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.

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