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Instability of the Dirichlet problem for Hamilton-Jacobi equation

Published online by Cambridge University Press:  17 April 2009

Kewei Zhang
Kewei Zhang
Affiliation:
Department of Mathematics, Heriot-Watt University, Richarton, Edinburgh EH14 4AS, United Kingdom e-mail: kewei@ma.hw.ac.uk
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We show the instability of solutions of the Dirichlet problem for Hamilton-Jacobi equations under quite general conditions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 311 - 319
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Adams, R.A., Sobolev spaces (Academic Press, New York, 1975).Google Scholar
[2]Barles, G., Solutions de viscosité des équations de Hamilton-Jacobi (Springer-Verlag, Berlin, Heidelberg, New York, 1994).Google Scholar
[3]Ball, J.M., ‘A version of the fundamental theorem for Young measures’, in Lecture Notes in Physics 344 (Springer-Verlag, Berlin, Heidelberg, New York, 1988), pp. 207–215.Google Scholar
[4]Barnes, I., Zhang, K.-W., ‘Instability of the eikonal equation and shape from shading’, (in preparation).Google Scholar
[5]Carlotto, M.J., ‘Digital imagery analysis of unusual Martian surface features’, Appl. Optics 27 (1988), 1926–1933.CrossRefGoogle Scholar
[6]Chabrowski, J., Zhang, K.-W., ‘On shape from shading problem’, in Functional Analysis, Approximation Theory and Numerical Analysis, (Rassias, J.M., Editor) (World Scientific, 1994), pp. 93–105.CrossRefGoogle Scholar
[7]Chabrowski, J., Zhang, K.-W., ‘On variational approach to the Hamilton-Jacobi PDE’, Comment. Math. Univ. Carolin. 34 (1993), 613–633.Google Scholar
[8]Horn, B.K.P. and Brooks, M.J., Shape from shading, (Horn, B.K.P. and Brooks, M.J., Editors), Artificial Intelligence (MIT Press, 1989).Google Scholar
[9]Lions, P.L., Generalized solutions of Hamilton-Jacobi equations (Pitman, London, 1982).Google Scholar
[10]Lions, P.L., Rouy, E., Tourin, A., ‘Shape-from-shading, viscosity solutions and edges’, Numer. Math. 64 (1993), 323–353.CrossRefGoogle Scholar
[11]Rouy, E., Tourin, A., ‘A viscosity solution approach to shape-from-shading’, SIAM J. Numer. Anal. 29 (1992), 867–884.CrossRefGoogle Scholar
[12]Tartar, L., ‘Compensated compactness and applications to partial differential equations’, in Nonlinear Analysis and Mechanics, (Knops, R., Editor), Heriot-Watt Symposium IV (Pitman, 1979), pp. 136–212.Google Scholar