Volume mean densities for the heat equation
نویسنده
چکیده
It is shown that, for solid caps D of heat balls in Rd+1 with center z0 = (0, 0), there exist Borel measurable functions w on D such that inf w(D) > 0 and ∫ v(z)w(z) dz ≤ v(z0), for every supertemperature v on a neighborhood of D. This disproves a conjecture by N. Suzuki and N.A. Watson. On the other hand, it turns out that there is no such volume mean density, if the bounded domain D in Rd × (−∞, 0) is only slightly wider at z0 than a heat ball.
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