Mean value densities for temperatures

Volume 98 / 2003

N. Suzuki, N. A. Watson Colloquium Mathematicum 98 (2003), 87-96 MSC: Primary 35K05; Secondary 31B05. DOI: 10.4064/cm98-1-7

Abstract

A positive measurable function $K$ on a domain $D$ in ${{\mathbb R}}^{n+1}$ is called a mean value density for temperatures if $u(0,0) = \int \int _D K(x,t)u(x,t)\, dx\, dt$ for all temperatures $u$ on $\, \overline {\! D}$. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on $D$ is also discussed.

Authors

  • N. SuzukiGraduate School of Mathematics
    Nagoya University
    Nagoya, Japan
    e-mail
  • N. A. WatsonDepartment of Mathematics and Statistics
    University of Canterbury
    Christchurch, New Zealand
    e-mail

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