Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes

We continue the study of viscosity solutions of Hamilton–Jacobi equations in metric spaces initiated in [ 37 ]. We present a more complete account of the theory of metric viscosity solutions based on local slopes. Several comparison and existence results are proved and the main techniques for such m...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2015-09, Vol.54 (1), p.1183-1218
Main Authors: Gangbo, Wilfrid, Święch, Andrzej
Format: Article
Language:English
Subjects:
Analysis
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Hamilton-Jacobi equation
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Metric space
Partial differential equations
Slopes
Systems Theory
Theoretical
Viscosity
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Summary:We continue the study of viscosity solutions of Hamilton–Jacobi equations in metric spaces initiated in [ 37 ]. We present a more complete account of the theory of metric viscosity solutions based on local slopes. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-015-0822-5