Green functions for second order parabolic integro-differential problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Harlow
Longman, Scientific & Techn.
1992
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman research notes in mathematics series
275 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 417 S. |
| ISBN: | 0582021561 |
Internformat
MARC
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| 100 | 1 | |a Garroni, Maria G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Green functions for second order parabolic integro-differential problems |c M. G. Garroni and J. L. Menaldi |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow |b Longman, Scientific & Techn. |c 1992 | |
| 300 | |a 417 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 275 | |
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Datensatz im Suchindex
| _version_ | 1804120382429462528 |
|---|---|
| adam_text | Contents
I Background 1
1.1 Introductory Material 1
1.1.1 Definitions of Basic Function Spaces 2
1.1.2 Some Basic Results 8
1.2 Existence and Uniqueness Results 18
1.3 Classic Maximum Principles 26
1.4 Markov Feller Processes 33
1.4.1 Preliminaries 33
1.4.2 Definitions and Main Properties 35
1.4.3 Some Standard Examples 41
1.4.4 Extensions 43
1.4.5 Ito s Formula 46
II Integro Differential Parabolic Equations 49
II. 1 Definition of the Integro Differential Operator 50
II. 1.1 Discussion 50
II.1.2 In the Whole Space 52
II. 1.3 In a Bounded Domain 62
II. 1.4 In a Unbounded Domain 66
11.2 Maximum Principles 71
11.3 Existence and Uniqueness Results 88
11.4 Stochastic Interpretation 96
III A Simple Cauchy Problem 101
III. 1 Wiener and Poisson Processes 101
111.2 Essential Properties 104
111.3 Dirichlet Neumann Problems in Half space Ill
111.3.1 Some Basic Properties 113
111.3.2 Construction of a Simple Green Function 118
III.4 Stochastic Representation 124
IV Green and Poisson Functions 127
IV.1 Definition of a Fundamental Solution 128
IV.1.1 Heat Equation 128
IV.1.2 Definition and Main Properties 134
IV.2 Definition of a Green Function 143
IV.2.1 Discussion 143
IV.2.2 Definition and Main Properties 146
IV.3 Definition of a Poisson Function 154
V Fundamental Solutions for Differential Equations 159
V.I Estimates for the Heat Potentials 161
V.2 Operators with Constant Coefficients 169
V.2.1 Constant Coefficients 169
V.2.2 Coefficients Depending on Parameters 172
V.3 Variable Coefficients 175
V.3.1 General Techniques 176
V.3.2 The Parametrix Method 178
V.4 The Cauchy Problem 187
V.5 Layer Potentials 191
V.5.1 Single Layer Potential: Neumann Problem 192
V.5.2 Double Layer Potential: Dirichlet Problem 201
V.5.3 Single Layer Potential: Oblique Derivative 203
VI Classic Green and Poisson Functions 209
VI.l Problems in Half Space 211
VI.1.1 Poisson Function for the Heat Equation 211
VI. 1.2 Green Function for the Heat Equation 216
VI.l.3 The Case of Constant Coefficients 223
VI. 1.4 Estimates of Superficial Potentials 233
VI.1.5 The Case of Variable Coefficients 235
VI.2 First and Second Boundary Value Problems 242
VI.2.1 Dirichlet Boundary Conditions 242
VI.2.2 Neumann Boundary Conditions 250
VI.3 Oblique Derivative Boundary Conditions 251
VI.3.1 Position of the Problem and Main Results 251
VI.3.2 The Reference Function 255
VI.3.3 Weighted Exponential Estimates 259
VI.3.4 The Solution Function 261
VI.3.5 Some Auxiliary Inequalities 267
VII Green Spaces 277
VII.1 Definition of the Function Spaces 278
VII.2 An Integral Transformation 284
VII.3 Properties of the Integra differential Operator 295
VII.3.1 Zero Order 295
VII.3.2 Positive Order 301
VII.4 Commutative Property 314
VIII The Construction of the Green Function 319
VIII.1 Volterra Equations 321
VIII.2 Existence of the Green Function 335
VIII.3 Reflected Diffusion Processes with Jumps 344
IX Estimates on the Green Function 353
IX.l First Order Estimates 355
IX.2 Singular Integral Estimates 357
IX.3 Integro Differential Operator Estimates 378
IX.4 Second Order Estimates 389
Bibliography 409
|
| any_adam_object | 1 |
| author | Garroni, Maria G. Menaldi, Jose L. |
| author_facet | Garroni, Maria G. Menaldi, Jose L. |
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| author_sort | Garroni, Maria G. |
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| building | Verbundindex |
| bvnumber | BV006154191 |
| classification_rvk | SI 880 SK 580 SK 620 SK 560 |
| ctrlnum | (OCoLC)246852259 (DE-599)BVBBV006154191 |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV006154191 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:41:12Z |
| institution | BVB |
| isbn | 0582021561 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003892274 |
| oclc_num | 246852259 |
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| owner_facet | DE-384 DE-739 DE-12 DE-355 DE-BY-UBR DE-706 DE-11 DE-188 DE-20 |
| physical | 417 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Longman, Scientific & Techn. |
| record_format | marc |
| series | Pitman research notes in mathematics series |
| series2 | Pitman research notes in mathematics series |
| spelling | Garroni, Maria G. Verfasser aut Green functions for second order parabolic integro-differential problems M. G. Garroni and J. L. Menaldi 1. publ. Harlow Longman, Scientific & Techn. 1992 417 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 275 Green-Funktion - Integrodifferentialgleichung - Parabolische Differentialgleichung - Ordnung 2 Green-Funktion (DE-588)4158123-4 gnd rswk-swf Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Integrodifferentialgleichung (DE-588)4161939-0 gnd rswk-swf Green-Funktion (DE-588)4158123-4 s Integrodifferentialgleichung (DE-588)4161939-0 s Ordnung 2 (DE-588)4350619-7 s DE-604 Menaldi, Jose L. Verfasser aut Pitman research notes in mathematics series 275 (DE-604)BV000022845 275 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003892274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garroni, Maria G. Menaldi, Jose L. Green functions for second order parabolic integro-differential problems Pitman research notes in mathematics series Green-Funktion - Integrodifferentialgleichung - Parabolische Differentialgleichung - Ordnung 2 Green-Funktion (DE-588)4158123-4 gnd Ordnung 2 (DE-588)4350619-7 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| subject_GND | (DE-588)4158123-4 (DE-588)4350619-7 (DE-588)4161939-0 |
| title | Green functions for second order parabolic integro-differential problems |
| title_auth | Green functions for second order parabolic integro-differential problems |
| title_exact_search | Green functions for second order parabolic integro-differential problems |
| title_full | Green functions for second order parabolic integro-differential problems M. G. Garroni and J. L. Menaldi |
| title_fullStr | Green functions for second order parabolic integro-differential problems M. G. Garroni and J. L. Menaldi |
| title_full_unstemmed | Green functions for second order parabolic integro-differential problems M. G. Garroni and J. L. Menaldi |
| title_short | Green functions for second order parabolic integro-differential problems |
| title_sort | green functions for second order parabolic integro differential problems |
| topic | Green-Funktion - Integrodifferentialgleichung - Parabolische Differentialgleichung - Ordnung 2 Green-Funktion (DE-588)4158123-4 gnd Ordnung 2 (DE-588)4350619-7 gnd Integrodifferentialgleichung (DE-588)4161939-0 gnd |
| topic_facet | Green-Funktion - Integrodifferentialgleichung - Parabolische Differentialgleichung - Ordnung 2 Green-Funktion Ordnung 2 Integrodifferentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003892274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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