On parabolic measures and subparabolic functions
Author:
Jang Mei G. Wu
Journal:
Trans. Amer. Math. Soc. 251 (1979), 171-185
MSC:
Primary 31C99; Secondary 31D05, 35K99
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531974-X
Erratum:
Trans. Amer. Math. Soc. 259 (1980), 636-636.
MathSciNet review:
531974
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Abstract | References | Similar Articles | Additional Information
Abstract: Let D be a domain in and
be the parabolic boundary of D. Suppose
is composed of two parts B and S: B is given locally by
and S is given locally by the graph of
where f is Lip 1 with respect to the local space variables and Lip
with respect to the universal time variable. Let
be the n-dimensional Hausdorff measure in
and
be the
-dimensional Hausdorff measure in
. And let
for
.
We study (i) the relation between the parabolic measure on and the measure dm on
and (ii) the boundary behavior of subparabolic functions on D.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1979-0531974-X
Keywords:
Lipschitz domain,
heat equation,
parabolic measure,
parabolic function,
subparabolic function,
Green's function,
Schauder estimates,
Harnack inequality,
maximum principle,
Brownian trajectories
Article copyright:
© Copyright 1979
American Mathematical Society