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Removable Lateral Singularities of Semilinear Parabolic PDEs and Besov Capacities

โœ Scribed by S.E Kuznetsov

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
288 KB
Volume
156
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Suppose 1<: 2, L is a second-order elliptic differential operator in R d and D is a bounded smooth domain in R d . Let Q=R + _D and let 1 be a compact set on the lateral boundary of Q. We prove that 1 is a removable lateral singularity for the equation u* +Lu=u : in Q if and only if Cap 1ร‚:, 2ร‚:, :$ (1 )=0 where Cap stands for the Besov capacity on the boundary.

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Polar boundary sets for superdiffusions
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โœ S. E. Kuznetsov ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 363 KB

Suppose L is a second-order elliptic differential operator in R d and D is a bounded, smooth domain in R d . Let 1 < ฮฑ โ‰ค 2 and let ฮ“ be a closed subset of โˆ‚D. It is known [13] that the following three properties are equivalent: (ฮฑ) ฮ“ is โˆ‚-polar; that is, ฮ“ is not hit by the range of the correspondi