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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
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] 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
  • [3] 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 and Los Angeles, 1951, pp. 189–215. MR 0045333
  • [4] A. Prékopa, On logarithmic concave measures and functions, Acta Sci. Math. 34 (1972), 336-343.

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Article copyright: © Copyright 1979 American Mathematical Society

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