Hausdorff continuous viscosity solutions of hamilton-jacobi equations

Authors:
R. Anguelov;S. Markov;F. Minani
Affiliations:
Department of Mathematics and Applied Mathematics, University of Pretoria;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences;Department of Applied Mathematics, National University of Rwanda
Venue:
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Year:
2009

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Abstract

A new concept of viscosity solutions, namely, the Hausdorff continuous viscosity solution for the Hamilton-Jacobi equation is defined and investigated It is shown that the main ideas within the classical theory of continuous viscosity solutions can be extended to the wider space of Hausdorff continuous functions while also generalizing some of the existing concepts of discontinuous solutions.