Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations-Reference-Cited by-同舟云学术

Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

Published:2020-08-06 Issue:4 Volume:20 Page:769-781
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Dai Limei¹,Bao Jiguang²

Affiliation:

1. School of Mathematics and Information Science , Weifang University , Weifang , Shandong 261061 , P. R. China

2. School of Mathematical Sciences , Beijing Normal University , Laboratory of Mathematics and Complex Systems, Ministry of Education , Beijing 100875 , P. R. China

Abstract

Abstract In this paper, we study the Cauchy problem of the parabolic Monge–Ampère equation

- u t ⁢ det ⁡ D 2 ⁢ u = f ⁢ ( x , t )

-u_{t}\det D^{2}u=f(x,t)

and obtain the existence and uniqueness of viscosity solutions with asymptotic behavior by using the Perron method.

Funder

Natural Science Foundation of Shandong Province

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2020-2102/pdf

Reference19 articles.

1. L. Caffarelli and Y. Li, Some multi-valued solutions to Monge–Ampère equations, Comm. Anal. Geom. 14 (2006), no. 3, 411–441.

2. L. Caffarelli, Y. Li and L. Nirenberg, Some remarks on singular solutions of nonlinear elliptic equations. I, J. Fixed Point Theory Appl. 5 (2009), no. 2, 353–395.

3. L. Caffarelli, Y. Li and L. Nirenberg, Some remarks on singular solutions of nonlinear elliptic equations. II. Symmetry and monotonicity via moving planes, Advances in Geometric Analysis, Adv. Lect. Math. (ALM) 21, International Press, Somerville (2012), 97–105.

4. L. Caffarelli, Y. Li and L. Nirenberg, Some remarks on singular solutions of nonlinear elliptic equations III: Viscosity solutions including parabolic operators, Comm. Pure Appl. Math. 66 (2013), no. 1, 109–143.

5. L. Dai, Exterior problems of parabolic Monge–Ampère equations for n=2n=2, Comput. Math. Appl. 67 (2014), no. 8, 1497–1506.

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