Asymptotics of potentials in the edge calculus
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 145-182.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

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. 
@article{BUMI_2006_8_9B_1_a7,
     author = {Kapanadze, D. and Schulze, B.-W},
     title = {Asymptotics of potentials in the edge calculus},
     journal = {Bollettino della Unione matematica italiana},
     pages = {145--182},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {1},
     year = {2006},
     zbl = {1118.58014},
     mrnumber = {2204905},
     language = {it},
     url = {https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_1_a7/}
}
TY  - JOUR
AU  - Kapanadze, D.
AU  - Schulze, B.-W
TI  - Asymptotics of potentials in the edge calculus
JO  - Bollettino della Unione matematica italiana
PY  - 2006
SP  - 145
EP  - 182
VL  - 9B
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_1_a7/
LA  - it
ID  - BUMI_2006_8_9B_1_a7
ER  - 
%0 Journal Article
%A Kapanadze, D.
%A Schulze, B.-W
%T Asymptotics of potentials in the edge calculus
%J Bollettino della Unione matematica italiana
%D 2006
%P 145-182
%V 9B
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_1_a7/
%G it
%F BUMI_2006_8_9B_1_a7
Kapanadze, D.; Schulze, B.-W. Asymptotics of potentials in the edge calculus. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 1, pp. 145-182. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_1_a7/

[1] S. Agmon - A. Douglis - L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math., 12 (1959), 623-727, 17 (1964), 35-92. | fulltext (doi) | MR | Zbl

[2] L. Boutet De Monvel, Boundary problems for pseudo-differential operators, Acta Math., 126 (1971), 11-51. | fulltext (doi) | MR | Zbl

[3] O. Chkadua - R. Duduchava, Asymptotics of functions represented by potentials, Russian Journal of Mathem. Physics, 7 (2000), 15-47. | MR | Zbl

[4] J. B. Gil - B.-W. Schulze - J. Seiler, Cone pseudodifferential operators in the edge symbolic calculus, Osaka J. Math., 37 (2000), 219-258. | MR

[5] M. Dauge, Elliptic boundary value problems on corner domains, Lecture Notes in Mathematics, vol. 1341, Springer-Verlag, 1988. | fulltext (doi) | MR | Zbl

[6] D. Kapanadze - B.-W. Schulze, Crack theory and edge singularities, Kluwer Academic Publ., Dordrecht, 2003. | fulltext (doi) | MR | Zbl

[7] N. Dines - B.-W. Schulze, Mellin-edge-representation of elliptic operators, Math. Meth. in the Applied Sci. (to appear). | fulltext (doi) | MR | Zbl

[8] V.A. Kondratyev, Boundary value problems for elliptic equations in domains with conical points, Trudy Mosk. Mat. Obshch., 16 (1967), 209-292. | MR

[9] E. Schrohe - B.-W. Schulze, A symbol algebra for pseudodifferential boundary value problems on manifolds with edges, Differential Equations, Asymptotic Analysis, and Mathematical Physics, Math. Research, vol. 100 (Akademie Verlag, Berlin, 1997), 292-324. | MR | Zbl

[10] E. Schrohe - B.-W. Schulze, Boundary value problems in Boutet de Monvel's calculus for manifolds with conical singularities I, Advances in Partial Differential Equations (Pseudo-differential calculus and Mathematical Physics) (Akademie Verlag, Berlin, 1994), 97-209. | MR

[11] E. Schrohe - B.-W. Schulze, Boundary value problems in Boutet de Monvel's calculus for manifolds with conical singularities II, Advances in Partial Differential Equations (Boundary Value Problems, Schrodinger Operators, Deformation Quantization) (Akademie Verlag, Berlin, 1995), 70-205. | MR | Zbl

[12] B.-W. Schulze, Pseudo-differential operators on manifolds with singularities, North-Holland, Amsterdam, 1991. | MR

[13] B.-W. Schulze, Boundary value problems and singular pseudo-differential operators, J. Wiley, Chichester, 1998. | MR

[14] B.-W. Schulze, Crack theory with singularities at the boundary, Pliska Stud. Math. Bulgar., 15 (2003), 21-66. | MR

[15] B.-W. Schulze - J. Seiler, The edge algebra structure of boundary value problems, Annals of Global Analysis and Geometry, 22 (2002), 197-265. | fulltext (doi) | MR | Zbl

[16] B.-W. Schulze - N.N. Tarkhanov, Green pseudodifferential operators on a manifold with edges, Comm. Partial Differential Equations, 23, 1-2 (1998), 171-200. | fulltext (doi) | MR

[17] J. Seiler, The cone algebra and kernel characterization of Green operators, Advances in Partial Differential Equations (Approaches to Singular Analysis) (J. Gil, D. Grieser, and Lesch M., eds.), Oper. Theory Adv. Appl. (Birkhäuser, Basel, 2001), 1-29. | MR | Zbl