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The Jump of the Laplacian on a Submanifold

โœ Scribed by Ewa Dudek; Konstanty Holly

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
388 KB
Volume
188
Category
Article
ISSN
0025-584X

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โœฆ Synopsis

Assume that a submanifold M C Rn of an arbitrary codimension k E { 1,. . . , n} is closed in some open set 0 C IR". With a given function ZL E C2(0 \ M) we may associate its trivial extension ii : 0 + IR such that tIlo~ = u and ~I M 0 . The jump of the Laplacian of the function ZL on the submanifold M is defined by the distribution Aa -Au. By applying some general version of the F'ubini theorem to the nonlinear projection onto M we obtain the formula for the jump of the Laplacian (Theorem 2.2).

๐Ÿ“œ SIMILAR VOLUMES

The Divergence on Submanifolds of the Wi
The Divergence on Submanifolds of the Wiener Space
โœ J. Vanbiesen ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 1023 KB

Using Malliavin's calculus, the divergence, the covariant derivative, and the Riemann and Ricci curvatures of a submanifold of the Wiener space are defined. It is shown that the Ricci and Riemann curvatures appear in the commutator of the divergence operator and covariant derivative operator. Capaci