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GENERALIZED MEAN VALUE PROPERTY FOR CALORIC FUNCTIONS

    https://doi.org/10.1142/9789812794253_0105Cited by:0 (Source: Crossref)
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    Abstract:

    In this note we discuss a generalized mean value property

    for given functions f and μ, and all integrable caloric functions h in Ω.

    The particular case of f ≡ 1 and μ being the Dirac delta function supported in would give rise to the corresponding mean value property for harmonic functions, provided the above integral identity holds for some Ω ⊂ ℝn+1 and caloric functions h in Ω.