A note on parabolic convexity and heat conduction

Christer Borell

Annales de l'I.H.P. Probabilités et statistiques (1996)

  • Volume: 32, Issue: 3, page 387-393
  • ISSN: 0246-0203

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Borell, Christer. "A note on parabolic convexity and heat conduction." Annales de l'I.H.P. Probabilités et statistiques 32.3 (1996): 387-393. <http://eudml.org/doc/77540>.

@article{Borell1996,
author = {Borell, Christer},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {parabolic convexity; Brownian motion; Ehrhard inequality},
language = {eng},
number = {3},
pages = {387-393},
publisher = {Gauthier-Villars},
title = {A note on parabolic convexity and heat conduction},
url = {http://eudml.org/doc/77540},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Borell, Christer
TI - A note on parabolic convexity and heat conduction
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1996
PB - Gauthier-Villars
VL - 32
IS - 3
SP - 387
EP - 393
LA - eng
KW - parabolic convexity; Brownian motion; Ehrhard inequality
UR - http://eudml.org/doc/77540
ER -

References

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  2. [2] C. Borell, Undersökning av paraboliska mått. Preprint series No. 16, Aarhus Univ. 1974/75. MR388475
  3. [3] C. Borell, Geometric properties of some familiar diffusions in Rn. Ann. Probability, Vol. 21, 1993, pp. 482-489. Zbl0776.35024MR1207234
  4. [4] C. Borell, Greenian potentials and concavity. Math. Ann., 1985, pp. 155-160 . Zbl0584.31003MR794098
  5. [5] H.J. Brascamp and E.H. Lieb, In Functional integration and its applications, edited by A. M. Arthurs, Clarendon Press, Oxford1975. Zbl0348.26011MR465645
  6. [6] H.J. Brascamp and E.H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation.J. Funct. Anal., Vol. 22, 1976, pp. 366-389. Zbl0334.26009MR450480
  7. [7] J.L. Doob, Classical potential theory and its probabilistic counterpart, Springer-Verlag, New York, 1984. Zbl0549.31001MR731258
  8. [8] A. Ehrhard, Symétrisation dans l'espace deGauss. Math. Scand., Vol. 53, 1983, pp. 281-301. Zbl0542.60003MR745081
  9. [9] R.M. Gabriel, A result concerning convex level surfaces of 3-dimensional harmonic functions. J. London Math. Soc., Vol. 32, 1957, pp. 286-294. Zbl0087.09702MR90662
  10. [10] L. Hörmander, Notions of convexity, Birkhäuser, Boston, 1994. Zbl0835.32001MR1301332
  11. [11] B. Kawohl, When are superharmonic functions concave? Applications to the St. Venant torsion problem and to the fundamental mode of the clamped membrane.Z. Angew. Math. Mech., Vol. 64, 1984, pp. 364-366. Zbl0581.73006MR754534
  12. [12] N.A. Watson, Green functions, potentials, and the Dirichlet problem for the heat equation. Proc. London Math. Soc., Vol. 33, 1976, pp. 251-298. Zbl0336.35046MR425145
  13. [13] N.A. Watson, Mean values of subtemperatures over level surfaces of Green functions. Ark. Mat., Vol. 30, 1992, pp. 165-185. Zbl0784.35039MR1171101

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