Displaying similar documents to “Caloric measure and Reifenberg flatness.”

Sets of determination for parabolic functions on a half-space

Jarmila Ranošová (1994)

Commentationes Mathematicae Universitatis Carolinae

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We characterize all subsets M of ℝ n × ℝ + such that sup X ∈ ℝ n × ℝ + u ( X ) = sup X ∈ M u ( X ) for every bounded parabolic function u on ℝ n × ℝ + . The closely related problem of representing functions as sums of Weierstrass kernels corresponding to points of M is also considered. The results provide a parabolic counterpart to results for classical harmonic functions in a ball, see References. As a by-product the question of representability of probability continuous distributions as sums of multiples of normal distributions is investigated. ...

Characterization of sets of determination for parabolic functions on a slab by coparabolic (minimal) thinness

Jarmila Ranošová (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let T be a positive number or + ∞ . We characterize all subsets M of ℝ n × ] 0 , T [ such that inf X ∈ ℝ n × ] 0 , T [ u ( X ) = inf X ∈ M u ( X ) i for every positive parabolic function u on ℝ n × ] 0 , T [ in terms of coparabolic (minimal) thinness of the set M δ = ∪ ( x , t ) ∈ M B p ( ( x , t ) , δ t ) , where δ ∈ ( 0 , 1 ) and B p ( ( x , t ) , r ) is the “heat ball” with the “center” ( x , t ) and radius r . Examples of different types of sets which can be used instead of “heat balls” are given. It is proved that (i) is equivalent to the condition sup X ∈ ℝ n × ℝ + u ( X ) = sup X ∈ M u ( X ) for every bounded parabolic function on ℝ n × ℝ + and hence to all equivalent conditions given in the article...