Non-Homogeneous Boundary Value Problems and Applications
Vol. 1
Published on 15. November 2011
Book
Paperback/Softback
XVI, 360 pages
978-3-642-65163-2 (ISBN)
Description
1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1972
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XVI, 360 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 21 mm
Weight
575 gr
ISBN-13
978-3-642-65163-2 (9783642651632)
DOI
10.1007/978-3-642-65161-8
Schweitzer Classification
Other editions
Additional editions
Book
01/1972
Springer
€85.55
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Content
0.- 13. Intersection Interpolation.- 14. Holomorphic Interpolation.- 15. Another Intrinsic Definition of the Spaces [X, Y]0.- 16. Compactness Properties.- 17. Comments.- 18. Problems.- 2 Elliptic Operators. Hilbert Theory.- 1. Elliptic Operators and Regular Boundary Value Problems.- 2. Green's Formula and Adjoint Boundary Value Problems.- 3. The Regularity of Solutions of Elliptic Equations in the Interior of ?.- 4. A priori Estimates in the Half-Space.- 5. A priori Estimates in the Open Set ? and the Existence of Solutions in Hs(?)-Spaces, with Real s ? 2m.- 6. Application of Transposition: Existence of Solutions in Hs(?)-Spaces, with Real s ? 0.- 7. Application of Interpolation: Existence of Solutions in Hs(?)-Spaces, with Real s, 0 < s < 2m.- 8. Complements and Generalizations.- 9. Variational Theory of Boundary Value Problems.- 10. Comments.- 11. Problems.- 3 Variational Evolution Equations.- 1. An Isomorphism Theorem.- 2. Transposition.- 3. Interpolation.- 4. Example: Abstract Parabolic Equations, Initial Condition Problem (I).- 5. Example: Abstract Parabolic Equations, Initial Condition Problem (II).- 6. Example: Abstract Parabolic Equations, Periodic Solutions.- 7. Elliptic Regularization.- 8. Equations of the Second Order in t.- 9. Equations of the SecondOrder in t; Transposition.- 10. Schroedinger Type Equations.- 11. Schroedinger Type Equations; Transposition.- 12. Comments.- 13. Problems.