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

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- by Nam Q. Le and Ovidiu Savin PDF
- Proc. Amer. Math. Soc.
**143**(2015), 1605-1615 Request permission

## 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.## References

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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: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam; Department of Mathematics, Indiana University, Bloomington, IN 47405
- MR Author ID: 839112
- Email: nqle@indiana.edu
**Ovidiu Savin**- Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
- MR Author ID: 675185
- Email: savin@math.columbia.edu
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**143**(2015), 1605-1615 - MSC (2010): Primary 35J70, 35B65, 35B45, 35J96
- DOI: https://doi.org/10.1090/S0002-9939-2014-12340-9
- MathSciNet review: 3314073