A level set approach to semicontinuous viscosity solutions for Cauchy problems

Giga, Y.; Sato, M.-H

Hokkaido University Preprint Series in Mathematics, 1999, 472, 1-32

Permalink : https://doi.org/10.14943/83618

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DOI	https://doi.org/10.14943/83618
URI	https://hdl.handle.net/2115/69222
タイトル	A level set approach to semicontinuous viscosity solutions for Cauchy problems
著者	著者名 Giga, Y.
著者	著者名 Sato, M.-H
言語	英語
発行日	1999-09-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	472
ページ	1-32
抄録	A new notion of solution (called £-solution) is introduced so that the Cauchy problem for the Hamilton-Jacobi equation with semicontinuous initial data is globally solvable. No convexity assumptions on Hamiltonians are imposed. The solution is interpreted as the level set of an auxiliary problem. It turns out that our£solution is consistent with a classical discontinuous viscosity solution and a bitateral viscosity solution. Moreover, our L-solution is unique and enjoy the comparison principle. The condition that initial data is really attained is also discussed.
資源タイプ	紀要論文
出版タイプ	Version of Record