Differential and Integral Equations

Green's function of non-linear degenerate elliptic operators and its application to regularity

Zhaosheng Feng, Hanfang Lu, and Shenzhou Zheng

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We are concerned with the Green's function associated with the non-linear degenerate elliptic operator of divergence form. We present several theorems on local estimates and comparisons with the p-Laplacian for the Green's function under certain conditions in the sense of distributions. As an application of these estimates of the Green's function, the regularity in Morrey spaces of the so-called inhomogeneous A-harmonic equation is derived.

Article information

Differential Integral Equations, Volume 21, Number 7-8 (2008), 717-741.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J62: Quasilinear elliptic equations
Secondary: 35A08: Fundamental solutions 35B65: Smoothness and regularity of solutions 35J70: Degenerate elliptic equations 35J92: Quasilinear elliptic equations with p-Laplacian


Feng, Zhaosheng; Zheng, Shenzhou; Lu, Hanfang. Green's function of non-linear degenerate elliptic operators and its application to regularity. Differential Integral Equations 21 (2008), no. 7-8, 717--741. https://projecteuclid.org/euclid.die/1356038620

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