Crack Theory and Edge Singularities - Softcover

Inhaltsangabe

Preface. Introduction. 1: Boundary value problems with the transmission property. 1.1. Symbolic calculus and pseudo-differential operators. 1.2. Parameter-dependent boundary value problems. 1.3. General kernel cut-off constructions. 1.4. Notes and complementary remarks. 2: Operators on manifolds with conical singularities. 2.1. Mellin operators and cone asymptotics. 2.2. The cone algebra. 2.3. Analytic functionals and asymptotics. 2.4. Notes and complementary remarks. 3: Operators on manifolds with exits to infinity. 3.1. Scalar operators. 3.2. Calculus with operator-valued symbols. 3.3. Boundary value problems on manifolds with exits to infinity. 3.4. Notes and complementary remarks. 4: Boundary value problems on manifolds with edges. 4.1. Manifolds with edges and typical operators. 4.2. Weighted Sobolov spaces. 4.3. Operator conventions in the edge pseudo-differential calculus. 4.4. Operator-valued edge symbols. 4.5. The algebra of edge boundary value problems. 4.6. Further material on edge operators. 4.7. Notes and complementary remarks. 5: Crack theory. 5.1. Differential operators in crack configurations. 5.2. Parameter-dependent calculus in the model cone. 5.3. Local crack theory. 5.4. The global calculus. 5.5. Notes and complementary remarks. Bibliography. List of Symbols. Index.

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