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On the regularity of solutions to fully nonlinear elliptic equations via the Liouville property

Author(s): Qingbo Huang
Journal: Proc. Amer. Math. Soc. 130 (2002), 1955-1959.
MSC (2000): Primary 35J60; Secondary 35B65
Posted: February 8, 2002
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Abstract: We show that any $C^{1,1}$ solution to the uniformly elliptic equation $F(D^{2}u)=0$must belong to $C^{2,\alpha }$, if the equation has the Liouville property.

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Additional Information:

Qingbo Huang
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics & Statistics, Wright State University, Dayton, Ohio 45435
Email: qhuang@math.utexas.edu, qhuang@math.wright.edu

DOI: 10.1090/S0002-9939-02-06503-6
PII: S 0002-9939(02)06503-6
Keywords: Fully nonlinear elliptic equation, regularity, Liouville property, VMO
Received by editor(s): September 20, 1999
Posted: February 8, 2002
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2002, American Mathematical Society

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