Partial differential equations of elliptic type:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1970
|
| Edition: | 2. rev. ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
Neue Folge ; 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Einheitssacht.: Equazioni alle derivate parziali di tipo ellittico <engl.> - Aus d. Ital. übers. |
| Physical Description: | 370 S. |
Staff View
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| 240 | 1 | 0 | |a Equazioni alle derivate parziali di tipo ellittico |
| 245 | 1 | 0 | |a Partial differential equations of elliptic type |c Carlo Miranda |
| 250 | |a 2. rev. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1970 | |
| 300 | |a 370 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : Neue Folge |v 2 | |
| 500 | |a Einheitssacht.: Equazioni alle derivate parziali di tipo ellittico <engl.> - Aus d. Ital. übers. | ||
| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
| _version_ | 1804136091011252224 |
|---|---|
| adam_text | Contents
Chapter I. Boundary value problems for linear equations .... 1
1. Sets of points; functions 1
2. Elliptic equations 5
3. Maximum and minimum properties of the solutions of
elliptic equations 6
4. Various types of boundary value problems 8
5. Uniqueness theorems 10
6. Green s formula 12
7. Compatibility conditions for the boundary value problems;
other uniqueness theorems 14
8. Levi functions 17
9. Stokes s formula 19
10. Fundamental solutions; Green s functions 20
Chapter II. Functions represented by integrals 23
11. Products of composition of two kernels 23
12. Functions represented by integrals 24
13. Generalized domain potentials 28
14. Generalized single layer potentials 32
15. Generalized double layer potentials 39
16. Construction of functions satisfying assigned boundary con¬
ditions 43
Chapter III. Transformation of the boundary value problems into
integral equations 49
17. Review of basic knowledge about integral equations ... 49
18. The method of potentials 54
19. Existence of fundamental solutions. Unique continuation
property 59
20. Principal fundamental solutions 67
21. Transformation of the Dirichlet problem into integral
equations 73
22. Transformation of Neumann s problem into integral
equations 82
Contents XI
23. Transformation of the oblique derivative problem into
integral equations 86
24. The method of the quasi Green s functions 92
Chapter IV Generalized solutions of the boundary value problems . 97
25. Generalized elliptic operators 97
26. Equations with singular coefficients and known terms 100
27. Local properties of the solutions of elliptic equations ... 104
28. Generalized solutions according to Wiener of Dirichlet s
problem 108
29. Generalized boundary conditions 110
30. Weak solutions of the boundary value problems .... 121
81. The method of Fischer Riesz equations 134
82. The method of the minimum 143
Chapter V. A priori majorization of the solutions of the boundary
value problems 146
38. Orders of magnitude of the successive derivatives of a
function and of their Holder coefficients 147
84. Majorization in C(n A) of the solutions of equations with
constant coefficients 151
35. General majorization formulas in C( A) 154
86. Method of continuation for the proof of the existence
theorem for Dirichlet s problem 164
87. General majorization formulas in Hk* 169
38. Existence and regularization theorems 175
89. A priori bounds for the solutions of the second and third
boundary value problem 179
Chapter VI. Nonlinear equations 180
40. General properties of the solutions 181
41. Functional equations in abstract spaces 188
42. Dirichlet s problem for equations in m variables 194
43. Dirichlet s problem for equations in two variables .... 208
44. Equations in the analytic field 212
45. Equations in parametric form 217
46. The Neumann and oblique derivative problems 219
47. Equations of particular type 221
Chapter VII. Other research on equations of second order. Equa¬
tions of higher order. Systems of equations 223
48. Second order equations on a manifold 223
XII Contents
49. Second order equations in unbounded domains 225
50. Other problems for second order equations 233
51. Inverse problems and axiomatic theory for second order
equations 242
52. Equations of higher order 243
A. Elliptic operators of higher order 244
B. Green s formula. Fundamental solutions. Cauchy s
problem and the unique continuation property . . . 245
C. Local properties of the solutions 249
D. Dirichlet s and general boundary value problems . . . 249
E. Equations on manifolds. Pseudo differential operators.
Non local boundary problems 259
F. Equations in unbounded domains 260
G. Equations in regions with degenerate boundary . . . 261
H. Mixed and transmission problems 261
I. Polyharmonic functions 262
J. Nonlinear equations. Questions of analyticity .... 264
53. Systems of equations of the first order 265
54. Canonical form of elliptic equations 273
55. Systems of higher order equations 275
A. Elliptic systems 275
B. Green s formula. Fundamental matrix. Cauchy s
problem and the unique continuation property .... 276
C. Boundary value problems 278
D. Systems of second order equations 281
E. Systems on manifolds. Pseudo differential operators . . 282
F. Systems on unbounded domains.Transmission problems 283
G. Systems of equations from mathematical physics . . . 283
H. Nonlinear systems. Questions of analyticity 285
56. Degenerate elliptic equations. Questions of a small para¬
meter 285
Bibliography 289
Author Index 858
Subject Index 865
|
| adam_txt |
Contents
Chapter I. Boundary value problems for linear equations . 1
1. Sets of points; functions 1
2. Elliptic equations 5
3. Maximum and minimum properties of the solutions of
elliptic equations 6
4. Various types of boundary value problems 8
5. Uniqueness theorems 10
6. Green's formula 12
7. Compatibility conditions for the boundary value problems;
other uniqueness theorems 14
8. Levi functions 17
9. Stokes's formula 19
10. Fundamental solutions; Green's functions 20
Chapter II. Functions represented by integrals 23
11. Products of composition of two kernels 23
12. Functions represented by integrals 24
13. Generalized domain potentials 28
14. Generalized single layer potentials 32
15. Generalized double layer potentials 39
16. Construction of functions satisfying assigned boundary con¬
ditions 43
Chapter III. Transformation of the boundary value problems into
integral equations 49
17. Review of basic knowledge about integral equations . 49
18. The method of potentials 54
19. Existence of fundamental solutions. Unique continuation
property 59
20. Principal fundamental solutions 67
21. Transformation of the Dirichlet problem into integral
equations 73
22. Transformation of Neumann's problem into integral
equations 82
Contents XI
23. Transformation of the oblique derivative problem into
integral equations 86
24. The method of the quasi Green's functions 92
Chapter IV Generalized solutions of the boundary value problems . 97
25. Generalized elliptic operators 97
26. Equations with singular coefficients and known terms 100
27. Local properties of the solutions of elliptic equations . 104
28. Generalized solutions according to Wiener of Dirichlet's
problem 108
29. Generalized boundary conditions 110
30. Weak solutions of the boundary value problems . 121
81. The method of Fischer Riesz equations 134
82. The method of the minimum 143
Chapter V. A priori majorization of the solutions of the boundary
value problems 146
38. Orders of magnitude of the successive derivatives of a
function and of their Holder coefficients 147
84. Majorization in C(n'A) of the solutions of equations with
constant coefficients 151
35. General majorization formulas in C("A) 154
86. Method of continuation for the proof of the existence
theorem for Dirichlet's problem 164
87. General majorization formulas in Hk* 169
38. Existence and regularization theorems 175
89. A priori bounds for the solutions of the second and third
boundary value problem 179
Chapter VI. Nonlinear equations 180
40. General properties of the solutions 181
41. Functional equations in abstract spaces 188
42. Dirichlet's problem for equations in m variables 194
43. Dirichlet's problem for equations in two variables . 208
44. Equations in the analytic field 212
45. Equations in parametric form 217
46. The Neumann and oblique derivative problems 219
47. Equations of particular type 221
Chapter VII. Other research on equations of second order. Equa¬
tions of higher order. Systems of equations 223
48. Second order equations on a manifold 223
XII Contents
49. Second order equations in unbounded domains 225
50. Other problems for second order equations 233
51. Inverse problems and axiomatic theory for second order
equations 242
52. Equations of higher order 243
A. Elliptic operators of higher order 244
B. Green's formula. Fundamental solutions. Cauchy's
problem and the unique continuation property . . . 245
C. Local properties of the solutions 249
D. Dirichlet's and general boundary value problems . . . 249
E. Equations on manifolds. Pseudo differential operators.
Non local boundary problems 259
F. Equations in unbounded domains 260
G. Equations in regions with degenerate boundary . . . 261
H. Mixed and transmission problems 261
I. Polyharmonic functions 262
J. Nonlinear equations. Questions of analyticity . 264
53. Systems of equations of the first order 265
54. Canonical form of elliptic equations 273
55. Systems of higher order equations 275
A. Elliptic systems 275
B. Green's formula. Fundamental matrix. Cauchy's
problem and the unique continuation property . 276
C. Boundary value problems 278
D. Systems of second order equations 281
E. Systems on manifolds. Pseudo differential operators . . 282
F. Systems on unbounded domains.Transmission problems 283
G. Systems of equations from mathematical physics . . . 283
H. Nonlinear systems. Questions of analyticity 285
56. Degenerate elliptic equations. Questions of a small para¬
meter 285
Bibliography 289
Author Index 858
Subject Index 865 |
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| author | Miranda, Carlo 1912-1982 |
| author_GND | (DE-588)1074379950 |
| author_facet | Miranda, Carlo 1912-1982 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. rev. ed. |
| format | Book |
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| id | DE-604.BV022117192 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:02Z |
| indexdate | 2024-07-09T20:50:53Z |
| institution | BVB |
| language | English |
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| owner | DE-706 DE-188 |
| owner_facet | DE-706 DE-188 |
| physical | 370 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : Neue Folge |
| spelling | Miranda, Carlo 1912-1982 Verfasser (DE-588)1074379950 aut Equazioni alle derivate parziali di tipo ellittico Partial differential equations of elliptic type Carlo Miranda 2. rev. ed. New York [u.a.] Springer 1970 370 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : Neue Folge 2 Einheitssacht.: Equazioni alle derivate parziali di tipo ellittico <engl.> - Aus d. Ital. übers. Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Elliptische Differentialgleichung (DE-588)4014485-9 s Ergebnisse der Mathematik und ihrer Grenzgebiete Neue Folge ; 2 (DE-604)BV005871160 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Miranda, Carlo 1912-1982 Partial differential equations of elliptic type Ergebnisse der Mathematik und ihrer Grenzgebiete Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4014485-9 (DE-588)4044779-0 |
| title | Partial differential equations of elliptic type |
| title_alt | Equazioni alle derivate parziali di tipo ellittico |
| title_auth | Partial differential equations of elliptic type |
| title_exact_search | Partial differential equations of elliptic type |
| title_exact_search_txtP | Partial differential equations of elliptic type |
| title_full | Partial differential equations of elliptic type Carlo Miranda |
| title_fullStr | Partial differential equations of elliptic type Carlo Miranda |
| title_full_unstemmed | Partial differential equations of elliptic type Carlo Miranda |
| title_short | Partial differential equations of elliptic type |
| title_sort | partial differential equations of elliptic type |
| topic | Differential equations, Partial Elliptische Differentialgleichung (DE-588)4014485-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Differential equations, Partial Elliptische Differentialgleichung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332056&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT mirandacarlo equazioniallederivateparzialiditipoellittico AT mirandacarlo partialdifferentialequationsofelliptictype |