Multiple integrals in the calculus of variations:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Edition: | reprint. of the 1966 ed. |
| Series: | Classics in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 506 S. |
| ISBN: | 3540699155 9783540699156 |
Staff View
MARC
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| 100 | 1 | |a Morrey, Charles B. |d 1907-1984 |e Verfasser |0 (DE-588)172264332 |4 aut | |
| 245 | 1 | 0 | |a Multiple integrals in the calculus of variations |c Charles B. Morrey |
| 250 | |a reprint. of the 1966 ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a IX, 506 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Classics in mathematics | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017991141 | ||
Record in the Search Index
| _version_ | 1804139922161926144 |
|---|---|
| adam_text | Contents
Chapter l
Introduction
1.1. Introductory remarks
.....................
ι
1.2.
The plan of the book: notation
................. 2
1.3.
Very brief historical remarks
.................. 5
1.4.
The ErjLER equations
.....................
η
1.5.
Other classical necessary conditions
............... 10
1.6.
Classical sufficient conditions
.................. 12
1.7.
The direct methods
......................
15
1.8.
Lower semicontinuity
.....................
19
1.9.
Existence
........................... 23
1.10.
The differentiability theory. Introduction
............ 26
1.11.
Differentiability; reduction to linear equations
.......... 34
Chapter
2
Semi-classical results
2.1.
Introduction
......................... 39
2.2.
Elementary properties of harmonic functions
........... 40
2.3.
Weyl s lemma
........................ 41
2.4.
Poisson s integral formula; elementary
f
unctions
;
Green s functions
43
2.5.
Potentials
.......................... 47
2.6.
Generalized potential theory; singular integrals
.......... 48
2.7.
The Calderon-Zygmund inequalities
.............. 55
2.8.
The maximum principle for a linear elliptic equation of the second order
61
Chapter
3
The spaces H% and H%0
3.1.
Definitions and first theorems
.................. 62
3-2.
General boundary values; the spaces H™0{G); weak convergence.
. . 68
3.3.
The Diricblet problem
....................
70
3.4.
Boundary values
....................... 72
3.5.
Examples; continuity; some SoBOLEV lemmas
........... 78
3.6.
Miscellaneous additional results
................. 81
3.7.
Potentials and quasi-potentials; generalizations
.......... 86
viii Contents
Chapter
4
Existence theorems
4.1.
The lower-semicontinuity theorems of
Serrín
........... 90
4.2.
Variational problems with
ƒ = ƒ(#);
the equations
(1.10.13)
with
N — 1,
Bt = o,A* = Aa{j>)
...................... 98
4.3.
The borderline cases
k
=v
................... 105
4.4.
The general quasi-regular integral
................
H2
Chapter
5
Differentiability of weak solutions
5.1.
Introduction
......................... 126
5.2.
General theory; v>
2..................... 128
5.3.
Extensions of the
de
GiORGr-NASH-MosER results ;v
> 2 .....
і
34
5.4.
The case»
= 2........................ 143
5.5.
Lv and
Schauder
estimates
.................. 149
5.6.
The equation« -V2«
+
Ь
-V«
+
ou
—
Аи
—f
.......... 157
5.7.
Analytícity
of the solutions of analytic linear equations
...... 164
5.8.
Analyticity of the solutions of analytic, non-linear, elliptic equations
170
5.9.
Properties of the extremals; regular cases
............ 186
5.10.
The extremals in the case
1 <
к
< 2.............. 191
5.11.
The theory of Ladyzenskaya and Ural tseva
.......... 194
5.12.
A class of non-linear equations
................. 203
Chapter
6
Regularity theorems for the solutions of general
elliptic systems and boundary value problems
6.1.
Introduction
......................... 209
6.2.
Interior estimates for general elliptic systems
........... 215
6.3.
Estimates near the boundary; coerciveness
............ 225
6.4-
Weak solutions
........................ 242
6.5.
The existence theory for the Dirichlet problem for strongly elliptic
systems
........................... 251
6.6.
The analyticity of the solutions of analytic systems of linear elliptic
equations
.......................... 258
6.7.
The analyticity of the solutions of analytic nonlinear elliptic systems
266
6.8.
The differentiability of the solutions of non-linear elliptic systems;
weak solutions; a perturbation theorem
............. 277
Chapter
7
A variational method in the theory of harmonic integrals
7.1.
Introduction
......................... 286
7.2.
Fundamentals; the
Gaffney-GÅrding
inequality
......... 288
7.3.
The variational method
.................... 293
7-4-
The decomposition theorem. Final results for compact manifolds with¬
out boundary
......................... 295
7-5-
Manifolds with boundary
...................
300
7.6.
Differentiability at the boundary
................ 305
7.7·
Potentials, the decomposition theorem
..............
309
7.8.
Boundary value problems
...................
314
Contents ix
Chapter
8
The
Э
-Neümann
problem on strongly pseudo-convex manifolds
8.1.
Introduction
......................... 316
8.2.
Results. Examples. The analytic embedding theorem
....... 320
8.3.
Some important formulas
.................... 328
8.4.
The
Hiłbert
space results
................... 333
8.5.
The local analysis
... :................... 337
8.6.
The smoothness results
.................... 341
Chapter
9
Introduction to parametric Integrals; two dimensional problems
9-1.
Introduction. Parametric integrals
............... 34-9
9-2.
A lower semi-continuity theorem
................ 354
9-3·
Two dimensional problems; introduction; the
conformai
mapping of
surfaces
........................... 362
9A. The problem of Plateau
.................... 374
9·5·
The general two-dimensional parametric problem
......... 390
Chapter
10
The higher dimensional Plateau problems
10.1.
Introduction
......................... 400
10.2.
ν
surfaces, their boundaries, and their Hausdorff measures
.... 407
10-3.
The topological results of Adams
................ 414
10.4·
The minimizing sequence; the minimizing set
........... 421
10.5.
The local topological disc property
............... 439
10.6.
The
Heisenberg
cone inequality
................ 459
10.7.
The local differentiability
................... 474
10.8.
Additional results of Fbderek concerning Lebesgue v-area
..... 480
Bibliography
........................... 494
Index
.............................. 504
|
| any_adam_object | 1 |
| author | Morrey, Charles B. 1907-1984 |
| author_GND | (DE-588)172264332 |
| author_facet | Morrey, Charles B. 1907-1984 |
| author_role | aut |
| author_sort | Morrey, Charles B. 1907-1984 |
| author_variant | c b m cb cbm |
| building | Verbundindex |
| bvnumber | BV035714247 |
| classification_rvk | SK 660 |
| ctrlnum | (OCoLC)265730306 (DE-599)BVBBV035714247 |
| dewey-full | 515.64 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.64 |
| dewey-search | 515.64 |
| dewey-sort | 3515.64 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | reprint. of the 1966 ed. |
| format | Book |
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| id | DE-604.BV035714247 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:51:46Z |
| institution | BVB |
| isbn | 3540699155 9783540699156 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017991141 |
| oclc_num | 265730306 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | IX, 506 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Classics in mathematics |
| spelling | Morrey, Charles B. 1907-1984 Verfasser (DE-588)172264332 aut Multiple integrals in the calculus of variations Charles B. Morrey reprint. of the 1966 ed. Berlin [u.a.] Springer 2008 IX, 506 S. txt rdacontent n rdamedia nc rdacarrier Classics in mathematics Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Mehrfaches Integral (DE-588)4224692-1 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 s Mehrfaches Integral (DE-588)4224692-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017991141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morrey, Charles B. 1907-1984 Multiple integrals in the calculus of variations Variationsrechnung (DE-588)4062355-5 gnd Mehrfaches Integral (DE-588)4224692-1 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)4224692-1 |
| title | Multiple integrals in the calculus of variations |
| title_auth | Multiple integrals in the calculus of variations |
| title_exact_search | Multiple integrals in the calculus of variations |
| title_full | Multiple integrals in the calculus of variations Charles B. Morrey |
| title_fullStr | Multiple integrals in the calculus of variations Charles B. Morrey |
| title_full_unstemmed | Multiple integrals in the calculus of variations Charles B. Morrey |
| title_short | Multiple integrals in the calculus of variations |
| title_sort | multiple integrals in the calculus of variations |
| topic | Variationsrechnung (DE-588)4062355-5 gnd Mehrfaches Integral (DE-588)4224692-1 gnd |
| topic_facet | Variationsrechnung Mehrfaches Integral |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017991141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT morreycharlesb multipleintegralsinthecalculusofvariations |