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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: Shenzhou Zheng and Zhaosheng Feng
Journal: Trans. Amer. Math. Soc. 364 (2012), 3627-3655
MSC (2010): Primary 35J70, 35H20, 35D10
Published electronically: March 7, 2012
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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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Additional Information

Shenzhou Zheng
Affiliation: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
Email: shzhzheng@bjtu.edu.cn

Zhaosheng Feng
Affiliation: Department of Mathematics, University of Texas-Pan American, Edinburg, Texas 78539
Email: zsfeng@utpa.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05617-0
PII: S 0002-9947(2012)05617-0
Keywords: Green function, X-ellipticity, control distance, maximum principle, Morrey’s space, hole-filling technique
Received by editor(s): July 27, 2010
Published electronically: March 7, 2012
Additional Notes: This work was supported by NSF (China) Grant No.11071012 and UTPA Faculty Research Council Grant 145MATH04
The second author was the corresponding author
Article copyright: © Copyright 2012 American Mathematical Society