A sharp global estimate and an overdetermined problem for Monge-Ampère type equations-Reference-Cited by-同舟云学术

A sharp global estimate and an overdetermined problem for Monge-Ampère type equations

Published:2022-01-01 Issue:1 Volume:22 Page:1-14
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Mohammed Ahmed¹,Porru Giovanni²

Affiliation:

1. Department of Mathematical Sciences , Ball State University , Muncie , IN , USA

2. Dipartimento di Matematica e Informatica , University of Cagliari , Cagliari , Italy

Abstract

Abstract We consider Monge-Ampère type equations involving the gradient that are elliptic in the framework of convex functions. Through suitable symmetrization we find sharp estimates to solutions of such equations. An overdetermined problem related to our Monge-Ampère type operators is also considered and we show that such a problem may admit a solution only when the underlying domain is a ball.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0001/pdf

Reference21 articles.

1. B. Brandolini and C. Trombetti, A symmetrization result for Monge-Ampère type equations, Math. Nachr. 280 (2007), 467–478.

2. L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations III: Functions of eigenvalues of the Hessian, Acta Math., 155 (1985), 261–301.

3. C. Chen, X. Ma and S. Shi, Curvature estimates for the level sets of solutions to the Monge-Ampère equation D2u = 1, Chin. Ann. Math., Series B (2014), 895–906.

4. C. Enache, Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs, Nonlinear Differ. Equ. Appl. 17 (2010), 591–600.

5. A. Figalli, The Monge-Ampère Equation and Its Applications, Zurich Lectures in Advanced Mathematics.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Problems for generalized Monge–Ampère equations;Canadian Mathematical Bulletin;2023-09-11