A1 Journal article (refereed)
Convergence of dynamic programming principles for the p-Laplacian (2022)

del Teso, F., Manfredi, J. J., & Parviainen, M. (2022). Convergence of dynamic programming principles for the p-Laplacian. Advances in Calculus of Variations, 15(2), 191-212. https://doi.org/10.1515/acv-2019-0043

JYU authors or editors

Publication details

All authors or editors: del Teso, Félix; Manfredi, Juan J.; Parviainen, Mikko

Journal or series: Advances in Calculus of Variations

ISSN: 1864-8258

eISSN: 1864-8266

Publication year: 2022

Publication date: 19/03/2020

Volume: 15

Issue number: 2

Pages range: 191-212

Publisher: De Gruyter

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1515/acv-2019-0043

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68568

Publication is parallel published: https://arxiv.org/abs/1808.10154

Abstract

We provide a unified strategy to show that solutions of dynamic programming principles associated to the p-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

Keywords: partial differential equations; approximation; numerical methods

Free keywords: Dirichlet problem; dynamic programming principle; discrete approximations; asymptotic mean value properties; convergence; monotone approximations; viscosity solution; generalized viscosity solution; equivalent notions of solutions; numerical methods

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Ministry reporting: Yes

Reporting Year: 2022

Preliminary JUFO rating: 1