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AuthorEgorov, Yuri V. author
TitlePseudo-Differential Operators, Singularities, Applications [electronic resource] / by Yuri V. Egorov, Bert-Wolfgang Schulze
ImprintBasel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997
Connect tohttp://dx.doi.org/10.1007/978-3-0348-8900-1
Descript XIII, 353 p. online resource

CONTENT

1 Sobolev spaces -- 1.1 Fourier transform -- 1.2 The first definition of the Sobolev space -- 1.3 General definition of Sobolev spaces in ?n -- 1.4 Representation of a linear functional over Hs -- 1.5 Embedding theorems -- 1.6 Sobolev spaces in a domain -- 2 Pseudo-differential Operators -- 2.1 The algebra of differential operators -- 2.2 Basic properties of pseudo-differential operators -- 2.3 Calculus of pseudo-differential operators -- 2.4 Pseudo-differential operators on closed manifolds -- 2.5 Gรฅrding inequality -- 3 Elliptic pseudo-differential operators -- 3.1 Parametrices of the elliptic operators -- 3.2 Elliptic operators on a manifold -- 4 Elliptic boundary value problems -- 4.1 Model elliptic boundary value problems -- 4.2 Elliptic boundary value problems in a domain -- 5 Kondratievโ{128}{153}s theory -- 5.1 A model problem -- 5.2 The general problem -- 5.3 The boundary value problem in an infinite cone for operators with constant coefficients -- 5.4 Equations with variable coefficients in an infinite cone -- 5.5 The boundary value problem in a bounded domain -- 6 Non-elliptic operators; propagation of singularities -- 6.1 Canonical transformations and Fourier integral operators -- 6.2 Wave fronts of distributions -- 6.3 Wave fronts and Fourier integral operators -- 6.4 Propagation of singularities -- 6.5 The Cauchy problem for a strongly hyperbolic equation -- 7 Pseudo-differential operators on manifolds with conical and edge singularities; motivation and technical preparations -- 7.1 The general background -- 7.2 Parameter-dependent pseudo-differential operators and operator-valued Mellin symbols -- 8 Pseudo-differential operators on manifolds with conical singularities -- 8.1 The cone algebra with asymptotics -- 8.2 The algebra on the infinite cone -- 9 Pseudo-differential operators on manifolds with edges -- 9.1 Pseudo-differential operators with operator-valued symbols -- 9.2 The edge symbolic calculus -- 9.3 Edge pseudo-differential operators -- 9.4 Applications, examples and remarks


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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