Elliptic boundary value problems in the spaces of distributions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Mathematics and its applications
384 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 415 S. |
| ISBN: | 0792343034 |
Staff View
MARC
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| 100 | 1 | |a Rojtberg, Jakov A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elliptic boundary value problems in the spaces of distributions |c by Yakov Roitberg |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a XI, 415 S. | ||
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| 490 | 1 | |a Mathematics and its applications |v 384 | |
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Record in the Search Index
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| adam_text | COnTEIlTS
Preface ix
0. Introduction 1
0.1. Concept of Generalized Solution 1
0.2. Functional Spaces 3
0.3. Operators Associated with Boundary Value Problems in the Complete
Scale of Sobolev Type Spaces 6
0.4. Theorem on Complete Collection of Isomorphisms 9
0.5. Weak Solutions of Elliptic Problems 11
0.6. Traces of Generalized Solutions on the Boundary of the Domain 12
0.7. Local Increase in Smoothness of Generalized Solutions. Green s Function 14
0.8. Elliptic Problems with Power Singularities. Degenerating Elliptic Problems 15
0.9. About the Monograph 16
1. Functional Spaces 19
1.1. Notation. Spaces C, 5, and 5 19
1.2. Positive and Negative Banach Spaces 22
1.3. Spaces of Bessel Potentials (Liouville Classes) Hs p= HS P(E. ) 24
1.4. Spaces Hs r P= Hs r{]R ) (s, re R, 1 p oo) 27
1.5. Besov Spaces B* ^ B ^E 1) (1 /? * , se R) 29
1.6. Infinitely Smoothing Operators 32
1.7. Spaces H? p=H *(W) and //vr (E ) 37
1.8. Spaces H5 p(TRn+) (s 0, l p °°). Operator 0+ 41
1.9. Spaces HS P(R +) and Hs r (R +) and Their Dual Spaces 43
1.10. Space HS G) 50
1.11. Space BSI{dG) 53
1.12. Operator of Multiplication by a Function in Functional Spaces 55
v
vj Contents
1.13. Norms that Depend on a Parameter. Spaces BS {G) and WS G).
Imbedding Theorems 59
1.14. Method of Complex Interpolation. Interpolational Theorem 62
1.15. Noetherian Operators 64
2. Space Hs pM){Q) 69
2.1. Definition of the Space Hs p (r)(Q) 69
2.2. Operator 5 70
2.3. Action of Differential Operators upon the Elements of Hs p ( r)(Q.)
(in the Strong Sense) 74
2.4. Action of Differential Operators upon the Elements of Hs p (r)(Q.)
(in the Weak Sense) 80
2.5. A Modification of Lemma 2.3.1 83
3. Elliptic Boundary Value Problem 85
3.1. Elliptic Differential Expressions with Constant Coefficients.
Proper Ellipticity 85
3.2. Elliptic Boundary Value Problems in a Half Space. Lopatinsky Condition 87
3.3 Elliptic Boundary Value Problem in a Bounded Domain 92
4. Theorem on Complete Collection of Isomorphisms 95
4.1. Principal Theorems 95
4.2. Model Problem in a Half Space 101
4.3. Solvability of Problem (4.2.26) in //+ (E )= Hs+t p 106
4.4. Proof of Theorem 4.2.1 for s 1 //; 110
4.5. Proof of Theorem 4.2.1 for s e ] 1 lp, 2m + l/p[ 120
4.6. Proof of Theorem 4.2.1 for s 2m + 1 lp 125
4.7. Smoothing Operator in H*pM W+) 129
4.8. Regularizer of the Operator A = (L,Bv...,Bm) 132
4.9. Completion of the Proof of Theorem 4.1.3 142
5. Elliptic Problems with Normal Boundary Conditions 145
5.1. Normal Systems of Boundary Expressions. Dirichlet Systems 145
5.2. Green s Formula 149
5.3. Regular Elliptic Problems and Adjoint Problems 153
5.4. Strong and Weak Solvability of Regular Elliptic Problems 160
5.5. Regular Elliptic Problems with Homogeneous Boundary Conditions 163
Contents vii
6. Traces of Generalized Solutions of Elliptic Equations on the Boundary
of the Domain 173
6.1. Traces of Generalized Solutions of Differential Equations in the Domain
with Nowhere Characteristic Boundary 173
6.2. Generalized Solutions Inside a Domain and Their Traces on the Boundary 182
6.3. Traces of Generalized Solutions on Surfaces Parallel to the Boundary 191
7. Local Increase in the Smoothness of Generalized Solutions of Elliptic
Boundary Value Problems. Green s Functions 213
7.1. Increase in the Smoothness of Generalized Solutions in the Entire Domain 213
7.2. Local Increase in Smoothness 215
7.3. Local Increase in the Smoothness of Generalized Solutions of Elliptic
Boundary Value Problems with Homogeneous Boundary Conditions 219
7.4. Green s Function 222
8. Elliptic Problems with Power Singularities on the Right Hand Sides.
Degenerate Elliptic Problems 249
8.1. Regularization of Functions with Point Singularities 250
8.2. Elliptic Problems with Point Power Singularities on the Right Hand Sides 258
8.3. Regularization of Functions with Power Singularities on / Dimensional
Manifolds (1 / « 1) 267
8.4. Elliptic Problems with Power Singularities on the Right Hand Sides
on / Dimensional Manifolds 273
8.5. Strongly Degenerate Elliptic Problems on / Dimensional Manifolds 288
9. Elliptic Boundary Value Problems with a Parameter 295
9.1. Definition of Elliptic Boundary Value Problems with a Parameter.
Formulation of the Principal Theorem 295
9.2. Model Problem 302
9.3. Proof of Theorem 9.1.1 310
9.4. Applications of Theorem 9.1.1 319
10. Elliptic Boundary Value Problems for Systems of Equations 323
10.1. Definition of an Elliptic Problem for a System. Principal Theorem 323
10.2. Model Problem in a Half Space 329
10.3. Proof of Theorem 10.1.1 355
10.4. Traces of Generalized Solutions of Systems of Equations 359
10.5. Local Increase in the Smoothness of Generalized Solutions of
Elliptic Systems 378
viii Contents
10.6. Other Applications of the Theorem on Complete Collection of
Isomorphisms for Elliptic Systems 381
Bibliographical Notes 385
References 393
Subject Index 413
Notation 415
|
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| id | DE-604.BV011250656 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:06:34Z |
| institution | BVB |
| isbn | 0792343034 |
| language | English |
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| physical | XI, 415 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Rojtberg, Jakov A. Verfasser aut Elliptic boundary value problems in the spaces of distributions by Yakov Roitberg Dordrecht [u.a.] Kluwer 1996 XI, 415 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 384 Distributionenraum (DE-588)4289272-7 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Distributionenraum (DE-588)4289272-7 s Elliptisches Randwertproblem (DE-588)4193399-0 s DE-604 Mathematics and its applications 384 (DE-604)BV008163334 384 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007552227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rojtberg, Jakov A. Elliptic boundary value problems in the spaces of distributions Mathematics and its applications Distributionenraum (DE-588)4289272-7 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4289272-7 (DE-588)4193399-0 |
| title | Elliptic boundary value problems in the spaces of distributions |
| title_auth | Elliptic boundary value problems in the spaces of distributions |
| title_exact_search | Elliptic boundary value problems in the spaces of distributions |
| title_full | Elliptic boundary value problems in the spaces of distributions by Yakov Roitberg |
| title_fullStr | Elliptic boundary value problems in the spaces of distributions by Yakov Roitberg |
| title_full_unstemmed | Elliptic boundary value problems in the spaces of distributions by Yakov Roitberg |
| title_short | Elliptic boundary value problems in the spaces of distributions |
| title_sort | elliptic boundary value problems in the spaces of distributions |
| topic | Distributionenraum (DE-588)4289272-7 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Distributionenraum Elliptisches Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007552227&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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