Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We show the instability of solutions of the Dirichlet problem for Hamilton-Jacobi equations under quite general conditions.
[1]Adams, R.A., Sobolev spaces (Academic Press, New York, 1975).Google Scholar
[2]
[2]Barles, G., Solutions de viscosité des équations de Hamilton-Jacobi (Springer-Verlag, Berlin, Heidelberg, New York, 1994).Google Scholar
[3]
[3]Ball, J.M., ‘A version of the fundamental theorem for Young measures’, in Lecture Notes in Physics344 (Springer-Verlag, Berlin, Heidelberg, New York, 1988), pp. 207–215.Google Scholar
[4]
[4]Barnes, I., Zhang, K.-W., ‘Instability of the eikonal equation and shape from shading’, (in preparation).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]
[11]Rouy, E., Tourin, A., ‘A viscosity solution approach to shape-from-shading’, SIAM J. Numer. Anal.29 (1992), 867–884.CrossRefGoogle Scholar
[12]
[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