A mean-value lemma and applications

Alessandro Savo

Bulletin de la Société Mathématique de France (2001)

  • Volume: 129, Issue: 4, page 505-542
  • ISSN: 0037-9484

Abstract

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We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write explicit bounds for the remainder term of the above expansion, which hold for all values of time. The results of this paper have been announced, without proof, in [16].

How to cite

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Savo, Alessandro. "A mean-value lemma and applications." Bulletin de la Société Mathématique de France 129.4 (2001): 505-542. <http://eudml.org/doc/272304>.

@article{Savo2001,
abstract = {We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write explicit bounds for the remainder term of the above expansion, which hold for all values of time. The results of this paper have been announced, without proof, in [16].},
author = {Savo, Alessandro},
journal = {Bulletin de la Société Mathématique de France},
keywords = {distance function; eigenvalues of the Laplace operator; heat equation; asymptotic expansions},
language = {eng},
number = {4},
pages = {505-542},
publisher = {Société mathématique de France},
title = {A mean-value lemma and applications},
url = {http://eudml.org/doc/272304},
volume = {129},
year = {2001},
}

TY - JOUR
AU - Savo, Alessandro
TI - A mean-value lemma and applications
JO - Bulletin de la Société Mathématique de France
PY - 2001
PB - Société mathématique de France
VL - 129
IS - 4
SP - 505
EP - 542
AB - We control the gap between the mean value of a function on a submanifold (or a point), and its mean value on any tube around the submanifold (in fact, we give the exact value of the second derivative of the gap). We apply this formula to obtain comparison theorems between eigenvalues of the Laplace-Beltrami operator, and then to compute the first three terms of the asymptotic time-expansion of a heat diffusion process on convex polyhedrons in euclidean spaces of arbitrary dimension. We also write explicit bounds for the remainder term of the above expansion, which hold for all values of time. The results of this paper have been announced, without proof, in [16].
LA - eng
KW - distance function; eigenvalues of the Laplace operator; heat equation; asymptotic expansions
UR - http://eudml.org/doc/272304
ER -

References

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