Mean value densities for temperatures
Volume 98 / 2003
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.
