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December  2003, 2(4): 447-459. doi: 10.3934/cpaa.2003.2.447

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, Italy
2. 

Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan

Received  April 2003 Revised  September 2003 Published  October 2003

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).
Keywords: Hamilton-Jacobi equations, differential games., semicontinuous viscosity solutions, Cauchy problem, right accessibility.
Mathematics Subject Classification: 35F25(primary), 49L2.
Citation: Martino Bardi, Yoshikazu Giga. Right accessibility of semicontinuous initial data for Hamilton-Jacobi equations. Communications on Pure and Applied Analysis, 2003, 2 (4) : 447-459. doi: 10.3934/cpaa.2003.2.447
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