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A maximum principle related to level surfaces of solutions of parabolic equations

Part of: Partial differential equations

Published online by Cambridge University Press:  09 April 2009

Carlo Pucci
Carlo Pucci
Affiliation:
Instituto Matematico, “Ulisse Dini”, Universita Degli Studi 50134, Firenze, Italy
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Abstract

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Let u be a solution of a parabolic equation ut = F(u, Du, D2u). Under convenient hypotheses it is proved that the angle between a given direction and the normal to the level surfaces of u(·,t) satisfies a maximum principle.

MSC classification

Secondary: 35B50: Maximum principles
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 1 , February 1989 , pp. 1 - 7
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Brascamp, H. J. and Lieb, E. H., ‘On extensions of the Brunn-Minkowski and PrékopaLendler theorems, including inequalities for log-concave functions, and with an application to the diffusion equation’, J. Funct. Anal. 22 (1976), 366–389.Google Scholar
[2]Gage, M. E., ‘An isoperimetric inequality with applications to curve shortening’, Duke Math. J. 50 (1983), 1225–1229.CrossRefGoogle Scholar
[3]Jones, C., ‘Spherically symmetric solutions of a reaction-diffusion equation’, J. Differential Equations 49 (1983), 42–169.CrossRefGoogle Scholar
[4]Matano, H., ‘Asymptotic behaviour and stability solutions of semilinear diffusion equations’, Publ. Res. Inst. Math. Sci. 15 (1979), 401–454.CrossRefGoogle Scholar
[5]Pucci, C., ‘An angle's maximum principle for the gradient of solutions of elliptic equations’, Boll. Un. Mat. Ital. A 1 (1987).Google Scholar
[6]Pucci, C., ‘An angle's maximum principle for the gradient of solutions of elliptic and parabolic equations’, Ist. Anal. Glob. C. N. R. Quad 17 (1987), 1–7.Google Scholar
[7]Tso, Kaising, ‘Deforming a hypersurface by its Gauss-Kronecker curvature’, Comm. Pure Appl. Math. 38 (1985), 867–882.Google Scholar