The logarithmic potential: discontinuous Dirichlet and Neumann problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
American Math. Soc.
2008
|
| Edition: | Repr. |
| Series: | Colloquium publications / American Mathematical Society
6 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 150 S. |
| ISBN: | 0821845993 9780821845998 |
Staff View
MARC
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| 100 | 1 | |a Evans, Griffith C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The logarithmic potential |b discontinuous Dirichlet and Neumann problems |c by Griffith Conrad Evans |
| 250 | |a Repr. | ||
| 264 | 1 | |a New York |b American Math. Soc. |c 2008 | |
| 300 | |a VIII, 150 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Colloquium publications / American Mathematical Society |v 6 | |
| 650 | 4 | |a Théorie du potentiel | |
| 650 | 4 | |a Équations différentielles | |
| 650 | 4 | |a Équations intégrales | |
| 650 | 0 | 7 | |a Logarithmisches Potenzial |0 (DE-588)4168046-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Logarithmisches Potenzial |0 (DE-588)4168046-7 |D s |
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Record in the Search Index
| _version_ | 1804142796771164160 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
Pages
I. Preliminary Concepts.
Stieltjes
Integrals and
Fourier Series
............................... 1
1.
Functions of limited variation.
2.
Continuation of
the preceding·.
3.
Integrals with respect to a function
of limited variation.
4.
Note on the second law of
the mean.
5.
Classical theorems on integrals and
limits of integrals.
6.
The limits of
Stieltjes
integrals.
7.
Note on Lebesgue integrals.
8.
Convergence of
Fourier series.
9.
Summability of series.
II. Functions Harmonic within a Circle
........... 26
10.
Preliminary theorems.
11.
A preliminary result.
12.
Note on integral identities.
13.
Digression:
Functions of points and of point sets.
І4.
Properties
of the Poisson-Stieltjes integral.
15.
Continuation
of the preceding: Behaviour of u(r,0) in the neighbor¬
hood of the boundary.
16.
The
Poisson
integral:
F
(φ)
absolutely continuous.
III. Necessary and Sufficient Conditions. The Dirichlet
Problems for the Circle
..................... 46
17.
Fundamental theorem and lemma.
18.
Proof
of fundamental theorem.
19.
Special cases of the
Poisson
integral.
20.
The Dirichlet problem and
its extension.
IV. Potentials of a Single Layer and the Neumann
Problem
..................................... 55
21.
The
Stieltjes
integral for potentials of a single
layer.
22.
Necessary and sufficient conditions.
23.
Further properties.
24.
The Neumann problems.
25.
General points of view.
26.
Digression: Phys¬
ical interpretation of a general distribution of mass.
27.
Cauchy s integral formula.
Pages
V. General Simply Connected Plane Eegions and the
Order of their Boundary Points
.............. 71
28.
Conformai
transformations and general regions.
29.
Invariant forms of conditions
(i), (ii)
etc.
30.
In¬
variant forms of conclusions.
31.
Order of boundary
points.
32.
Integrals on the boundary and the Dirichlet
problems.
33.
Special cases of the condition (ii). The
continuous boundary value problem.
34.
A new con¬
tinuous boundary value problem.
35.
The generalized
Neumann problem in the general region.
VI. Plane Eegions of Finite Connectivity
.......... 86
36.
Functions harmonic outside a circle.
37.
The
multiply connected region bounded by
и
-f
1
distinct
circles.
38.
Eepresentation in terms of the Green s
function.
39.
Boundary integrals and
Stieltjes
inte¬
gral equations.
40.
General regions of finite con¬
nectivity. Isolated point boundaries.
41.
Annular
regions. Determination of the functions
FQ(ß)
and
ί
(0). 42.
Uniqueness of the representation of Theo¬
rem
3
for S.
VII. Eelated
Problems
............................ 121
43.
A simple discontinuous boundary value problem.
44.
Continuous boundary value problems.
45
і
Eegions
with continuous boundaries.
46.
Eegions with recti-
fiable boundaries.
47.
Eegions of infinite connectivity.
48.
Eemarks on necessary and sufficient conditions.
49.
Convergence in the mean of positive order less
than one.
50.
Integro-differential equations of
Bôcher
type.
|
| any_adam_object | 1 |
| author | Evans, Griffith C. |
| author_facet | Evans, Griffith C. |
| author_role | aut |
| author_sort | Evans, Griffith C. |
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| bvnumber | BV036126221 |
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| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)319214811 (DE-599)BVBBV036126221 |
| discipline | Mathematik |
| edition | Repr. |
| format | Book |
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| id | DE-604.BV036126221 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:37:28Z |
| institution | BVB |
| isbn | 0821845993 9780821845998 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020208625 |
| oclc_num | 319214811 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | VIII, 150 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Math. Soc. |
| record_format | marc |
| series2 | Colloquium publications / American Mathematical Society |
| spelling | Evans, Griffith C. Verfasser aut The logarithmic potential discontinuous Dirichlet and Neumann problems by Griffith Conrad Evans Repr. New York American Math. Soc. 2008 VIII, 150 S. txt rdacontent n rdamedia nc rdacarrier Colloquium publications / American Mathematical Society 6 Théorie du potentiel Équations différentielles Équations intégrales Logarithmisches Potenzial (DE-588)4168046-7 gnd rswk-swf Logarithmisches Potenzial (DE-588)4168046-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3156-3 American Mathematical Society Colloquium publications 6 (DE-604)BV035417609 6 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020208625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evans, Griffith C. The logarithmic potential discontinuous Dirichlet and Neumann problems Théorie du potentiel Équations différentielles Équations intégrales Logarithmisches Potenzial (DE-588)4168046-7 gnd |
| subject_GND | (DE-588)4168046-7 |
| title | The logarithmic potential discontinuous Dirichlet and Neumann problems |
| title_auth | The logarithmic potential discontinuous Dirichlet and Neumann problems |
| title_exact_search | The logarithmic potential discontinuous Dirichlet and Neumann problems |
| title_full | The logarithmic potential discontinuous Dirichlet and Neumann problems by Griffith Conrad Evans |
| title_fullStr | The logarithmic potential discontinuous Dirichlet and Neumann problems by Griffith Conrad Evans |
| title_full_unstemmed | The logarithmic potential discontinuous Dirichlet and Neumann problems by Griffith Conrad Evans |
| title_short | The logarithmic potential |
| title_sort | the logarithmic potential discontinuous dirichlet and neumann problems |
| title_sub | discontinuous Dirichlet and Neumann problems |
| topic | Théorie du potentiel Équations différentielles Équations intégrales Logarithmisches Potenzial (DE-588)4168046-7 gnd |
| topic_facet | Théorie du potentiel Équations différentielles Équations intégrales Logarithmisches Potenzial |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020208625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035417609 |
| work_keys_str_mv | AT evansgriffithc thelogarithmicpotentialdiscontinuousdirichletandneumannproblems |