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Research Article | Open Access

Games associated with products of eigenvalues of the Hessian

Pablo Blanc1, Fernando Charro2, Juan J. Manfredi3( ), Julio D. Rossi1
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Department of Mathematics, Wayne State University, 656 W. Kirby, Detroit, MI 48202, USA
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
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Abstract

We introduce games associated with second-order partial differential equations given by arbitrary products of eigenvalues of the Hessian. We prove that, as a parameter that controls the step length goes to zero, the value functions of the games converge uniformly to a viscosity solution of the partial differential equation. The classical Monge-Ampère equation is an important example under consideration.

Keywords

eigenvalues of the HessiangamesMonge-Ampère equations

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Mathematics in Engineering
Volume 5 Issue 3,
June 2023
Pages 1-26
DOI: 10.3934/mine.2023066

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Cite this article:
Blanc P, Charro F, Manfredi JJ, et al. Games associated with products of eigenvalues of the Hessian. Mathematics in Engineering, 2023, 5(3): 1-26. https://doi.org/10.3934/mine.2023066

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Received: 23 September 2022
Revised: 15 November 2022
Accepted: 16 November 2022
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)