# Asymptotics of potentials in the edge calculus

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 1, page 145-182
- ISSN: 0392-4041

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topKapanadze, 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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