Green functions for a class of nonlinear degenerate operators with X-ellipticity

Zheng, Shenzhou; Feng, Zhaosheng

doi:10.1090/S0002-9947-2012-05617-0

Green functions for a class of nonlinear degenerate operators with X-ellipticity
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by Shenzhou Zheng and Zhaosheng Feng PDF

Trans. Amer. Math. Soc. 364 (2012), 3627-3655 Request permission

Abstract:

A maximum principle and some a priori estimates of a class of degenerate equations with X-ellipticity in the sense of distributions are established. A local comparison of the generalized Green function with its fundamental solutions is obtained. As an application, by means of the power of the Green function as a kernel function of a local integral, we also derive local Hölder continuity for nonlinear degenerate subelliptic equations.

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