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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, Volume 27, Number 3, Pages 237–245
DOI: https://doi.org/10.21538/0134-4889-2021-27-3-237-245 (Mi timm1852) 		 
A Survey of Hopf-Lax Formulas and Quasiconvexity in PDEs

E. N. Barron

Loyola University Chicago
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DOI: https://doi.org/10.21538/0134-4889-2021-27-3-237-245
Abstract: This is a short survey of recent results obtained by the author and collaborators primarily on Hopf-Lax formulas for Hamilton-Jacobi equations and obstacle problems. The initiation of the use of quasiconvex (i.e., level convex) functions in $L^\infty$ control and differential games led to such formulas and is briefly reviewed. Dedicated to the memory of Academician A. I. Subbotin.
Keywords: Hopf-Lax; viscosity solution; Hamilton-Jacobi; quasiconvex.
Received: 17.03.2021
Revised: 11.05.2021
Accepted: 24.05.2021
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 35C05,35D40,49L12,49N70
Language: English
Citation: E. N. Barron, “A Survey of Hopf-Lax Formulas and Quasiconvexity in PDEs”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 237–245
Citation in format AMSBIB
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\by E.~N.~Barron
\paper A Survey of Hopf-Lax Formulas and Quasiconvexity in PDEs
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 237--245
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