Asymptotic mean-value formulas for solutions of general second-order elliptic equations-Reference-Cited by-同舟云学术

Asymptotic mean-value formulas for solutions of general second-order elliptic equations

Published:2022-01-01 Issue:1 Volume:22 Page:118-142
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Blanc Pablo¹,Charro Fernando²,Manfredi Juan J.³,Rossi Julio D.⁴

Affiliation:

1. Department of Mathematics and Statistics, University of Jyväskylä , PO Box 35, FI-40014 , Jyväskylä , Finland

2. Department of Mathematics, Wayne State University , 656 W. Kirby , Detroit , MI 48202 , USA

3. Department of Mathematics, University of Pittsburgh , Pittsburgh , PA 15260 , USA

4. Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428) , Buenos Aires , Argentina

Abstract

Abstract We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2022-0007/pdf

Reference37 articles.

1. L. Ambrosio and H. M. Soner, Level set approach to mean curvature flow in arbitrary codimension, J. Differ. Geom. 43 (1996), 693–737.

2. A. R. Arroyo García, Nonlinear Mean Value Properties Related to the p-Laplacian, Ph.D. thesis, Universitat Autònoma de Barcelona, 2017.

3. I. Birindelli, G. Galise, and H. Ishii, Existence through convexity for the truncated Laplacians, Math. Ann. 379 (2021), 909–950.

4. P. Blanc, F. Charro, J. D. Rossi, J. J. Manfredi, A nonlinear Mean Value Property for the Monge-Ampère operator, J. Convex Anal. 28 (2021), no. 2, 353–386.

5. P. Blanc and J. D. Rossi, Games for eigenvalues of the Hessian and concave/convex envelopes, Jour. Math. Pures Appl. 127 (2019), 192–215.

Cited by 2 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. Nonlinear asymptotic mean value characterizations of holomorphic functions;ESAIM: Control, Optimisation and Calculus of Variations;2024

2. Asymptotic Average Solutions to Linear Second Order Semi-Elliptic PDEs: A Pizzetti-Type Theorem;Potential Analysis;2023-01-26