Integral Harnack inequality
1985 ◽
Vol 26
(2)
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pp. 115-120
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Keyword(s):
Let D be a domain in Euclidean space of d dimensions and K a compact subset of D. The well known Harnack inequality assures the existence of a positive constant A depending only on D and K such that (l/A)u(x)<u(y)<Au(x) for all x and y in K and all positive harmonic functions u on D. In this we obtain a global integral version of this inequality under geometrical conditions on the domain. The result is the following: suppose D is a Lipschitz domain satisfying the uniform exterior sphere condition—stated in Section 2. If u is harmonic in D with continuous boundary data f thenwhere ds is the d — 1 dimensional Hausdorff measure on the boundary ժD. A large class of domains satisfy this condition. Examples are C2-domains, convex domains, etc.
1996 ◽
Vol 53
(2)
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pp. 197-207
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1963 ◽
Vol 15
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pp. 157-168
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Keyword(s):
2004 ◽
Vol 56
(3)
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pp. 529-552
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Keyword(s):
2019 ◽
Vol 40
(12)
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pp. 3217-3235
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1946 ◽
Vol 42
(1)
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pp. 15-23
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Keyword(s):
1979 ◽
Vol 20
(2)
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pp. 147-154
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Keyword(s):
2021 ◽
Vol 60
(1)
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1989 ◽
Vol 31
(2)
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pp. 189-191
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Keyword(s):
1986 ◽
Vol 38
(6)
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pp. 1459-1484
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Keyword(s):