Asymptotics of potentials in the edge calculus

D. Kapanadze; B.-W Schulze

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 145-182
  • ISSN: 0392-4033

Abstract

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Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by submanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous operators between cone or edge Sobolev spaces and subspaces with asymptotics.

How to cite

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Kapanadze, D., and Schulze, B.-W. "Asymptotics of potentials in the edge calculus." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 145-182. <http://eudml.org/doc/289615>.

@article{Kapanadze2006,
abstract = {Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by submanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous operators between cone or edge Sobolev spaces and subspaces with asymptotics.},
author = {Kapanadze, D., Schulze, B.-W},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {145-182},
publisher = {Unione Matematica Italiana},
title = {Asymptotics of potentials in the edge calculus},
url = {http://eudml.org/doc/289615},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Kapanadze, D.
AU - Schulze, B.-W
TI - Asymptotics of potentials in the edge calculus
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 145
EP - 182
AB - Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by submanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous operators between cone or edge Sobolev spaces and subspaces with asymptotics.
LA - eng
UR - http://eudml.org/doc/289615
ER -

References

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