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Hokkaido University Preprint Series in Mathematics >
A level set approach to semicontinuous viscosity solutions for Cauchy problems
| Title: | A level set approach to semicontinuous viscosity solutions for Cauchy problems |
| Authors: | Giga, Y. Browse this author | | Sato, M.-H Browse this author |
| Issue Date: | 1-Sep-1999 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 472 |
| Start Page: | 1 |
| End Page: | 32 |
| Abstract: | 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69222 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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