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Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary
Author(s) -
Duduchava R.,
Speck F.O.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211600107
Subject(s) - mathematics , pseudodifferential operators , lipschitz continuity , bessel function , boundary (topology) , mathematical analysis , manifold (fluid mechanics) , pure mathematics , operator (biology) , order (exchange) , space (punctuation) , mechanical engineering , biochemistry , chemistry , finance , repressor , transcription factor , engineering , economics , gene , linguistics , philosophy
Pseudodifferential operators with non‐smooth symbols on a manifold M with Lipschitz boundary are considered. Theorems about order reduction and localization of such operators in Bessel potential H s pand Hölder‐Zygmund Z α p (IR n ) spaces are proved. A pseudodifferential operator A with locally sectorial matrix symbol is proved to be Fredholm in the space H s 2( M ) and Ind A = 0 where s depends on A. Application to a boundary value problem for an elastic body with crack is discussed in conclusion.