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Viscosity solutions and analysis in L∞

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Nonlinear Analysis, Differential Equations and Control

Part of the book series: NATO Science Series ((ASIC,volume 528))

Abstract

A systematic account of some results obtained in viscosity solutions, optimal control, and the variational theory of minimizing the maximum is presented. The major highlights include the theory of lower semicontinuous viscosity solutions, optimal control of the supremum, and its applications to explicit formulas for nonlinear partial differential equations. Several new results are presented including a new definition of Morrey convexity and Morrey quasiconvexity for vector valued problems, result on the existence of minimizers for nonquasiconvex supremands, a derivation of the Euler equation for minimax problems, and an application of minimax control to the minimal time function.

Supported in part by NSF grant DMS-9532030 and a grant from Loyola University

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Loyola University of Chicago, Chicago, IL, 60626, USA

    E. N. Barron

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  1. E. N. Barron
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Editors and Affiliations

  1. Institut Gérard Desargues, Université Claude Bernard (Lyon 1), Villeurbanne, France

    F. H. Clarke

  2. Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada

    R. J. Stern

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    G. Sabidussi

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Barron, E.N. (1999). Viscosity solutions and analysis in L∞. In: Clarke, F.H., Stern, R.J., Sabidussi, G. (eds) Nonlinear Analysis, Differential Equations and Control. NATO Science Series, vol 528. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4560-2_1

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  • DOI: https://doi.org/10.1007/978-94-011-4560-2_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5666-0

  • Online ISBN: 978-94-011-4560-2

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