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Logconcavity of the cooling of a convex body


Authors: Gilles Deslauriers and Serge Dubuc
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
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] K. Itô and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, New York, 1965. MR 0199891 (33:8031)
  • [3] M. Kac, On some connections between probability theory and differential and integral equations, Proc. Second Berkeley Symposium on Math. Statist. and Probability, Univ. of California Press, 1951, 189-215. MR 0045333 (13:568b)
  • [4] A. Prékopa, On logarithmic concave measures and functions, Acta Sci. Math. 34 (1972), 336-343.

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DOI: https://doi.org/10.1090/S0002-9939-1979-0524302-2
Article copyright: © Copyright 1979 American Mathematical Society

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