ITM Web Conf.
Volume 20, 2018International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|Number of page(s)||5|
|Section||Numerical and Applied Analysis|
|Published online||12 October 2018|
Gradient bounds for solutions of nonlinear strictly elliptic equations, applications and extensions
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
In this short manuscript, we briefly recall some well-known methods for obtaining gradient bounds of viscosity solutions for elliptic and parabolic equations. The two methods we focus here are the idea coming from Ishii- Lions’ method applies for strictly elliptic equations and the other one is socalled weak Bernstein’s method developed by Barles applies for degenerate equations. We present some results based on these methods and their applications. We also discuss some promising extensions in the future.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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