Logconcavity of the cooling of a convex body
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- by Gilles Deslauriers and Serge Dubuc PDF
- Proc. Amer. Math. Soc. 74 (1979), 291-294 Request permission
Abstract:
The solution $u(x,t)$ of the heat equation is logconcave in the space variable x whenever the initial temperature ${u_0}(x)$ of the convex body is logconcave.References
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H. J. Brascamp and E. H. Lieb, Some inequalities for Gaussian measures and the long-range order of the one-dimensional plasma, Functional Integration and its Applications, Clarendon Press, Oxford, 1975.
- Kiyoshi Itô and Henry P. McKean Jr., Diffusion processes and their sample paths, Die Grundlehren der mathematischen Wissenschaften, Band 125, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-New York, 1965. MR 0199891
- M. Kac, On some connections between probability theory and differential and integral equations, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 189–215. MR 0045333 A. Prékopa, On logarithmic concave measures and functions, Acta Sci. Math. 34 (1972), 336-343.
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 74 (1979), 291-294
- MSC: Primary 35K05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0524302-2
- MathSciNet review: 524302