Asymptotics of potentials in the edge calculus
Kapanadze, D. ; Schulze, B.-W
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 145-182 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

I problemi al contorno su varieta con singolarità coniche o di tipo edges (spigoli) contengono operatori potenziali come operatori di traccia e operatori di Green, i quali svolgono lo stesso ruolo dei corrispondenti operatori nel calcolo pseudo-differenziale per problemi al contorno su varietà lisce. Esiste allora uno specifico sviluppo asintotico di questi operatori nell'intorno delle singolarita. In questo lavoro caratteriziamo gli operatori potenziali in termini di azioni di operatori pseudodifferenziali di tipo conico o di tipo edge, su densità che sono supportate da sottovarietà che hanno anch'esse singolarità coniche e di tipo edge. Attravevso un biprodotto mostriamo che tali potenziali sono operatori continui tra spazi di Sobolev di tipo conico o di tipo edge e sottospazi con asintotiche.

Publié le : 2006-02-01
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     author = {D. Kapanadze and B.-W Schulze},
     title = {Asymptotics of potentials in the edge calculus},
     journal = {Bollettino dell'Unione Matematica Italiana},
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     year = {2006},
     pages = {145-182},
     zbl = {1118.58014},
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     language = {en},
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Kapanadze, D.; Schulze, B.-W. Asymptotics of potentials in the edge calculus. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 145-182. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_1_145_0/

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