International Journal of Differential Equations

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

Abstract

Carlson's type theorem on removable sets for $\alpha$-Holder continuous solutions is investigated for the quasilinear elliptic equations $\text{div} A\lleefftt(x,u,\nabla u\rrriiighttt)=0,$ having degeneration $\omega$ in the Muckenhoupt class. In partial, when $\alpha$ 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 ${\Lambda }_{\omega }^{-p+(p-1)\alpha }(E)=0$.

Article information

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

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

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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