Elliptic equations in polyhedral domains:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2010
|
| Series: | Mathematical surveys and monographs
162 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020461421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 589 - 597 |
| Physical Description: | VII, 608 S. graph. Darst. |
| ISBN: | 9780821849835 |
Staff View
MARC
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| 100 | 1 | |a Mazʹja, Vladimir Gilelevič |d 1937- |e Verfasser |0 (DE-588)121490602 |4 aut | |
| 245 | 1 | 0 | |a Elliptic equations in polyhedral domains |c Vladimir Maz'ya ; Jürgen Rossmann |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a VII, 608 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 162 | |
| 500 | |a Literaturverz. S. 589 - 597 | ||
| 650 | 0 | 7 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Polyedergebiet |0 (DE-588)4175160-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Differentialgleichung |0 (DE-588)4014485-9 |D s |
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| 830 | 0 | |a Mathematical surveys and monographs |v 162 |w (DE-604)BV000018014 |9 162 | |
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Record in the Search Index
| _version_ | 1829454806124593152 |
|---|---|
| adam_text |
Contents
Introduction
Part
1.
The Dirichlet problem for strongly elliptic systems in
polyhedral domains
7
Chapter
1.
Prerequisites on elliptic boundary value problems in domains with
conical points
9
1.1.
Elliptic boundary value problems in domains with smooth boundaries
9
1.2.
Elliptic boundary value problems in angles and cones
16
Chapter
2.
The Dirichlet problem for strongly elliptic systems in a dihedron
23
2.1.
Weighted Sobolev spaces in a dihedron
24
2.2.
Variational solutions of the Dirichlet problem
32
2.3.
The parameter-depending problem in a 2-dimensional wedge
39
2.4.
Solvability of the Dirichlet problem in weighted
L
-χ
Sobolev spaces
53
2.5.
Green's matrix of the Dirichlet problem in a dihedron
58
2.6.
Solvability in weighted Lp Sobolev spaces
64
2.7.
Weighted Holder spaces in a dihedron
72
2.8.
Solvability in weighted Holder spaces
75
2.9.
The problem with variable coefficients in a dihedron
81
Chapter
3.
The Dirichlet problem for strongly elliptic systems in a cone with
edges
89
3.1.
Weighted Sobolev spaces in a cone
90
3.2.
Operator pencils generated by the Dirichlet problem
96
3.3.
Solvability in weighted L2 Sobolev spaces
99
3.4.
Green's matrix of the Dirichlet problem in a cone
110
3.5.
Solvability in weighted LP Sobolev spaces
117
3.6.
Solvability in weighted Holder spaces
129
3.7.
The boundary value problem with variable coefficients in a cone
137
Chapter
4.
The Dirichlet problem in a bounded domain of polyhedral type
141
4.1.
Solvability of the boundary value problem in weighted Sobolev spaces
141
4.2.
Solvability of the boundary value problem in weighted Holder spaces
150
4.3.
Examples
153
Chapter
5.
The Miranda-Agmon maximum principle
161
5.1.
Green's matrix for the Dirichlet problem in a bounded domain
162
5.2.
The Miranda-Agmon maximum principle in domains of polyhedral
type
174
vi
CONTENTS
5.3.
The Miranda-Agmon maximum principle for generalized solutions in
domains with conical points
188
5.4.
The Miranda-Agmon maximum principle for smooth solutions in a
domain with a conical point
198
Part
2.
Neumann and mixed boundary value problems for second
order systems in polyhedral domains
211
Chapter
6.
Boundary value problems for second order systems in a dihedron
213
6.1.
Solvability in weighted Sobolev spaces with homogeneous norms
214
6.2.
Weighted Sobolev spaces with nonhomogeneous norms
222
6.3.
Parameter-dependent problems in an angle
239
6.4.
Solvability of the boundary value problem in the dihedron in weighted
Li Sobolev spaces
245
6.5.
Regularity results for solutions of the boundary value problem
251
6.6.
Green's matrix for the problem in the dihedron
262
6.7.
Weighted Holder spaces with nonhomogeneous norms
270
6.8.
Some estimates of the solutions in weighted Holder spaces
280
Chapter
7.
Boundary value problems for second order systems in a polyhedral
cone
289
7.1.
The boundary value problem and corresponding operator pencils
290
7.2.
Weighted Sobolev spaces in a cone
295
7.3.
Solvability of the boundary value problem in weighted
L-¿
Sobolev
spaces
298
7.4.
Regularity results for variational solutions
304
7.5.
Green's matrix of the boundary value problem in a polyhedral cone
310
7.6.
Solvability in weighted Lp Sobolev spaces
320
7.7.
Weak solutions in weighted Lp Sobolev spaces
326
7.8.
Solvability in weighted Holder spaces
339
Chapter
8.
Boundary value problems for second order systems in a bounded
polyhedral domain
355
8.1.
Solvability of the boundary value problem in weighted Sobolev spaces
355
8.2.
Solvability of the boundary value problem in weighted Holder spaces
368
8.3.
Examples
371
Part
3.
Mixed boundary value problems for stationary Stokes and
Navier-Stokes systems in polyhedral domains
379
Chapter
9.
Boundary value problem for the Stokes system in a dihedron
381
9.1.
Existence of weak solutions of the boundary value problem
382
9.2.
Compatibility conditions on the edge
388
9.3.
The model problem in an angle
394
9.4.
Solvability in weighted Li Sobolev spaces
400
9.5.
Green's matrix of the problems in a half-space
412
9.6.
Green's matrix for the boundary value problem in a dihedron
425
9.7.
Some estimates of solutions in weighted Holder spaces
433
CONTENTS
vii
Chapter
10.
Mixed boundary value problems for the Stokes system in a
polyhedral cone
443
10.1.
The boundary value problem and corresponding operator pencils
444
10.2.
Solvability of the boundary value problem in weighted L% Sobolev
spaces
448
10.3.
Regularity results for variational solutions
456
10.4.
Green's matrix of the boundary value problem in a cone
462
10.5.
Solvability of the boundary value problem in weighted Lp Sobolev
spaces
471
10.6.
Variational solutions of the boundary value problem in weighted Lp
Sobolev spaces
478
10.7.
Solvability in weighted Holder spaces
490
10.8.
Weak solutions in weighted Holder spaces
507
Chapter
11.
Mixed boundary value problems for the Stokes and Navier-Stokes
systems in a bounded domain of polyhedral type
519
11.1.
Mixed boundary value problems for the Stokes system
520
11.2.
Regularity results for solutions of the Navier-Stokes system
528
11.3.
Regularity results for particular boundary value problems
539
11.4.
Green's matrix of the Dirichlet problem for the Stokes system
544
11.5.
Green's matrix in a convex polyhedral domain
555
11.6.
Maximum modulus estimates for solutions of the Stokes and
Navier-Stokes system
568
Historical remarks
581
Bibliography
589
List of Symbols
599
List of Examples
605
Index
607 |
| any_adam_object | 1 |
| author | Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- |
| author_GND | (DE-588)121490602 (DE-588)122254856 |
| author_facet | Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- |
| author_role | aut aut |
| author_sort | Mazʹja, Vladimir Gilelevič 1937- |
| author_variant | v g m vg vgm j r jr |
| building | Verbundindex |
| bvnumber | BV036539625 |
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| dewey-full | 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3533 |
| dewey-search | 515.3533 |
| dewey-sort | 3515.3533 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036539625 |
| illustrated | Illustrated |
| indexdate | 2025-04-15T08:01:01Z |
| institution | BVB |
| isbn | 9780821849835 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020461421 |
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| owner_facet | DE-706 DE-355 DE-BY-UBR DE-29T |
| physical | VII, 608 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Mazʹja, Vladimir Gilelevič 1937- Verfasser (DE-588)121490602 aut Elliptic equations in polyhedral domains Vladimir Maz'ya ; Jürgen Rossmann Providence, RI American Math. Soc. 2010 VII, 608 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 162 Literaturverz. S. 589 - 597 Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Polyedergebiet (DE-588)4175160-7 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Polyedergebiet (DE-588)4175160-7 s DE-604 Roßmann, Jürgen 1954- Verfasser (DE-588)122254856 aut Erscheint auch als Online-Ausgabe 978-1-4704-1389-7 Mathematical surveys and monographs 162 (DE-604)BV000018014 162 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020461421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazʹja, Vladimir Gilelevič 1937- Roßmann, Jürgen 1954- Elliptic equations in polyhedral domains Mathematical surveys and monographs Elliptische Differentialgleichung (DE-588)4014485-9 gnd Polyedergebiet (DE-588)4175160-7 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4175160-7 |
| title | Elliptic equations in polyhedral domains |
| title_auth | Elliptic equations in polyhedral domains |
| title_exact_search | Elliptic equations in polyhedral domains |
| title_full | Elliptic equations in polyhedral domains Vladimir Maz'ya ; Jürgen Rossmann |
| title_fullStr | Elliptic equations in polyhedral domains Vladimir Maz'ya ; Jürgen Rossmann |
| title_full_unstemmed | Elliptic equations in polyhedral domains Vladimir Maz'ya ; Jürgen Rossmann |
| title_short | Elliptic equations in polyhedral domains |
| title_sort | elliptic equations in polyhedral domains |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd Polyedergebiet (DE-588)4175160-7 gnd |
| topic_facet | Elliptische Differentialgleichung Polyedergebiet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020461421&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT mazʹjavladimirgilelevic ellipticequationsinpolyhedraldomains AT roßmannjurgen ellipticequationsinpolyhedraldomains |