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Viscosity solutions of stationary Hamilton-Jacobi equations and minimizers of $ L^{\infty}$ functionals


Authors: E. N. Barron, M. Bocea and R. R. Jensen
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 35D40, 49J45, 52A41
DOI: https://doi.org/10.1090/proc/13668
Published electronically: June 28, 2017
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Abstract: Existence results for viscosity solutions to the Dirichlet problem for stationary Hamilton-Jacobi equations, the associated relaxed problem via quasiconvex envelopes, and for minimizers of the corresponding $ L^\infty $ functionals are obtained for given boundary data in $ W^{1,\infty }.$


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Additional Information

E. N. Barron
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60660
Email: ebarron@luc.edu

M. Bocea
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60660
Email: mbocea@luc.edu

R. R. Jensen
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60660
Email: rjensen@luc.edu

DOI: https://doi.org/10.1090/proc/13668
Keywords: Quasiconvex functions, viscosity solutions
Received by editor(s): August 10, 2016
Received by editor(s) in revised form: January 12, 2017
Published electronically: June 28, 2017
Additional Notes: This project was partially supported by the National Science Foundation under grant No. DMS-1515871
Communicated by: Joachim Krieger
Article copyright: © Copyright 2017 American Mathematical Society