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On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations


Authors: Nam Q. Le and Ovidiu Savin
Journal: Proc. Amer. Math. Soc. 143 (2015), 1605-1615
MSC (2010): Primary 35J70, 35B65, 35B45, 35J96
Published electronically: December 19, 2014
MathSciNet review: 3314073
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Abstract: In this paper, we establish boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations with $ L^{p}$ ( $ n<p\leq \infty $) right-hand side and $ C^{1,\gamma }$ boundary values under natural assumptions on the domain, boundary data and the Monge-Ampère measure. These estimates extend our previous boundary regularity results for solutions to the linearized Monge-Ampère equations with bounded right-hand side and $ C^{1, 1}$ boundary data.


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Additional Information

Nam Q. Le
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Address at time of publication: Department of Mathematics, Indiana University, Bloomington, IN 47405
Email: nqle@indiana.edu

Ovidiu Savin
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: savin@math.columbia.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12340-9
Keywords: Linearized Monge-Amp\`ere equations, localization theorem, boundary gradient estimates
Received by editor(s): May 17, 2013
Received by editor(s) in revised form: August 8, 2013
Published electronically: December 19, 2014
Communicated by: Joachim Krieger
Article copyright: © Copyright 2014 American Mathematical Society