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AuthorLions, J. L. author
TitleNon-Homogeneous Boundary Value Problems and Applications [electronic resource] : Volume III / by J. L. Lions, E. Magenes
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1973
Connect tohttp://dx.doi.org/10.1007/978-3-642-65393-3
Descript XII, 310 p. online resource

CONTENT

7 Scalar and Vector Ultra-Distributions -- 1. Scalar-Valued Functions of Class Mk -- 2. Scalar-Valued Ultra-Distributions of Class Mk; Generalizations -- 3. Spaces of Analytic Functions and of Analytic Functionals -- 4. Vector-Valued Functions of Class Mk -- 5. Vector-Valued Ultra-Distributions of Class Mk; Generalizations -- 6. Comments -- 8 Elliptic Boundary Value Problems in Spaces of Distributions and Ultra-Distributions -- 1. Regularity of Solutions of Elliptic Boundary Value Problems in Spaces of Analytic Functions and of Class Mk; Statement of the Problems and Results -- 2. The Theorem on โ{128}{156}Elliptic Iteratesโ{128}{157}: Proof -- 3. Application of Transposition; Existence of Solutions in the Space Dโ{128}{153}(?) of Distributions -- 4. Existence of Solutions in the Space $$D{'_{{M_k}}}\left( \Omega \right)$$ of Ultra-Distributions -- 5. Comments -- 6. Problems -- 9 Evolution Equations in Spaces of Distributions and Ultra-Distributions -- 1. Regularity Results. Equations of the First Order in t -- 2. Equations of the Second Order in t -- 3. Singular Equations of the Second Order in t -- 4. Schroedinger-Type Equations -- 5. Stability Results in Mk-Classes -- 6. Transposition -- 7. Semi-Groups -- 8. Mk -Classes and Laplace Transformation -- 9. General Operator Equations -- 10. The Case of a Finite Interval ]0, T[ -- 11. Distribution and Ultra-Distribution Semi-Groups -- 12. A General Local Existence Result -- 13. Comments -- 14. Problems -- 10 Parabolic Boundary Value Problems in Spaces of Ultra-Distributions -- 1. Regularity in the Interior of Solutions of Parabolic Equations -- 2. The Regularity at the Boundary of Solutions of Parabolic Boundary Value Problems -- 3. Application of Transposition: The Finite Cylinder Case -- 4. Application of Transposition: The Infinite Cylinder Case -- 5. Comments -- 6. Problems -- 11 Evolution Equations of the Second Order in t and of Schroedinger Type -- 1. Equations of the Second Order in t; Regularity of the Solutions of Boundary Value Problems -- 2. Equations of the Second Order in t; Application of Transposition and Existence of Solutions in Spaces of Distributions -- 3. Equations of the Second Order in t; Application of Transposition and Existence of Solutions in Spaces of Ultra-Distributions -- 4. Schroedinger Equations; Complements for Parabolic Equations -- 5. Comments -- 6. Problems -- Appendix. Calculus of Variations in Gevrey-Type Spaces


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