Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations

Martino Bardi; Yoshikazu Giga

doi:10.3934/cpaa.2003.2.447

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2003, Volume 2, Issue 4: 447-459. Doi: 10.3934/cpaa.2003.2.447

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Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations

Martino Bardi^1, and
Yoshikazu Giga^2,

1.
Dipartimento di Matematica P. e A., Universita di Padova, via Belzoni 7, 35131 Padova
2.
Department of Mathematics, Hokkaido University, Sapporo 060-0810

Received: April 2003

Revised: September 2003

Published: December 2003

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Abstract

We study Hamilton-Jacobi equations with upper semicontinuous initial data without convexity assumptions on the Hamiltonian. We analyse the behavior of generalized u.s.c solutions at the initial time $t=0$, and find necessary and sufficient conditions on the Hamiltonian such that the solution attains the initial data along a sequence (right accessibility).

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Mathematics Subject Classification: 35F25(primary), 49L25.

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