Holdings: Boundary value problems and Markov processes

Boundary value problems and Markov processes:

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Bibliographic Details
Main Author:	Taira, Kazuaki 1946- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2009
Edition:	2nd. ed.
Series:	Lecture notes in mathematics 1499
Subjects:	Feller-Halbgruppe Markov-Prozess Elliptisches Randwertproblem Semilineare parabolische Differentialgleichung Randwertproblem Elliptischer Differentialoperator Anfangswertproblem
Online Access:	Inhaltsverzeichnis
Physical Description:	XII, 186 S.
ISBN:	9783642016769

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MARC


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Record in the Search Index

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adam_text	CONTENTS 1 INTRODUCTION AND MAIN RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 SEMIGROUP THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 ANALYTIC SEMIGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 FRACTIONAL POWERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.3 THE SEMILINEAR CAUCHY PROBLEM . . . . . . . . . . . . . . . . . . . . 26 2.2 MARKOV PROCESSES AND FELLER SEMIGROUPS . . . . . . . . . . . . . . . . . . . 27 2.2.1 MARKOV PROCESSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.2 MARKOV TRANSITION FUNCTIONS. . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.3 PATH FUNCTIONS OF MARKOV PROCESSES . . . . . . . . . . . . . . . . . 35 2.2.4 STRONG MARKOV PROCESSES AND TRANSITION FUNCTIONS . . . . 36 2.2.6 GENERATION THEOREMS OF FELLER SEMIGROUPS. . . . . . . . . . . . 44 3 L P THEORY OF PSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . 55 3.1 FUNCTION SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 FOURIER INTEGRAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.1 SYMBOL CLASSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.2 PHASE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.3 OSCILLATORY INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3 PSEUDO-DIFFERENTIAL OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 L P APPROACH TO ELLIPTIC BOUNDARY VALUE PROBLEMS . . . . . . . . 77 4.1 THE DIRICHLET PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.2 FORMULATION OF A BOUNDARY VALUE PROBLEM. . . . . . . . . . . . . . . . . . 80 4.3 REDUCTION TO THE BOUNDARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5 PROOF OF THEOREM 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.1 BOUNDARY VALUE PROBLEM WITH SPECTRAL PARAMETER . . . . . . . . . . . 87 XI XII CONTENTS 6 A PRIORI ESTIMATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7 PROOF OF THEOREM 1.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.1 PROOF OF THEOREM 1.2, PART (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 7.1.1 PROOF OF PROPOSITION 7.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 7.2 PROOF OF THEOREM 1.2, PART (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 8 PROOF OF THEOREM 1.3, PART (I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.1 THE SPACE C 0 ( D M ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.2 SOBOLEV*S IMBEDDING THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.3 PROOF OF PART (I) OF THEOREM 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 9 PROOF OF THEOREM 1.3, PART (II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 9.1 GENERAL EXISTENCE THEOREM FOR FELLER SEMIGROUPS. . . . . . . . . . . . 125 9.2 FELLER SEMIGROUPS WITH REFLECTING BARRIER . . . . . . . . . . . . . . . . . . . 140 9.3 PROOF OF THEOREM 1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 9.4 PROOF OF PART (II) OF THEOREM 1.3 . . . . . . . . . . . . . . . . . . . . . . . . . . 159 10 APPLICATION TO SEMILINEAR INITIAL-BOUNDARY VALUE PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 10.1 LOCAL EXISTENCE AND UNIQUENESS THEOREMS . . . . . . . . . . . . . . . . . . 161 10.2 FRACTIONAL POWERS AND IMBEDDING THEOREMS . . . . . . . . . . . . . . . . 163 10.3 PROOF OF THEOREMS 10.1 AND 10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.3.1 PROOF OF THEOREM 10.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 10.3.2 PROOF OF THEOREM 10.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 11 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 A THE MAXIMUM PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
any_adam_object	1
author	Taira, Kazuaki 1946-
author_GND	(DE-588)120483858
author_facet	Taira, Kazuaki 1946-
author_role	aut
author_sort	Taira, Kazuaki 1946-
author_variant	k t kt
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dewey-full	519.233 515.353
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	519 - Probabilities and applied mathematics 515 - Analysis
dewey-raw	519.233 515.353
dewey-search	519.233 515.353
dewey-sort	3519.233
dewey-tens	510 - Mathematics
discipline	Mathematik
edition	2nd. ed.
format	Book
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series2	Lecture notes in mathematics
spelling	Taira, Kazuaki 1946- Verfasser (DE-588)120483858 aut Boundary value problems and Markov processes Kazuaki Taira 2nd. ed. Berlin [u.a.] Springer 2009 XII, 186 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1499 Feller-Halbgruppe (DE-588)4285866-5 gnd rswk-swf Markov-Prozess (DE-588)4134948-9 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Anfangswertproblem (DE-588)4001991-3 gnd rswk-swf Feller-Halbgruppe (DE-588)4285866-5 s Elliptischer Differentialoperator (DE-588)4140057-4 s Randwertproblem (DE-588)4048395-2 s Markov-Prozess (DE-588)4134948-9 s DE-604 Semilineare parabolische Differentialgleichung (DE-588)4180962-2 s Anfangswertproblem (DE-588)4001991-3 s Elliptisches Randwertproblem (DE-588)4193399-0 s 1\p DE-604 Lecture notes in mathematics 1499 (DE-604)BV000676446 1499 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017694926&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Taira, Kazuaki 1946- Boundary value problems and Markov processes Lecture notes in mathematics Feller-Halbgruppe (DE-588)4285866-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd Anfangswertproblem (DE-588)4001991-3 gnd
subject_GND	(DE-588)4285866-5 (DE-588)4134948-9 (DE-588)4193399-0 (DE-588)4180962-2 (DE-588)4048395-2 (DE-588)4140057-4 (DE-588)4001991-3
title	Boundary value problems and Markov processes
title_auth	Boundary value problems and Markov processes
title_exact_search	Boundary value problems and Markov processes
title_full	Boundary value problems and Markov processes Kazuaki Taira
title_fullStr	Boundary value problems and Markov processes Kazuaki Taira
title_full_unstemmed	Boundary value problems and Markov processes Kazuaki Taira
title_short	Boundary value problems and Markov processes
title_sort	boundary value problems and markov processes
topic	Feller-Halbgruppe (DE-588)4285866-5 gnd Markov-Prozess (DE-588)4134948-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd Semilineare parabolische Differentialgleichung (DE-588)4180962-2 gnd Randwertproblem (DE-588)4048395-2 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd Anfangswertproblem (DE-588)4001991-3 gnd
topic_facet	Feller-Halbgruppe Markov-Prozess Elliptisches Randwertproblem Semilineare parabolische Differentialgleichung Randwertproblem Elliptischer Differentialoperator Anfangswertproblem
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017694926&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000676446
work_keys_str_mv	AT tairakazuaki boundaryvalueproblemsandmarkovprocesses

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