Holdings: Elliptic partial differential equations

Elliptic partial differential equations: existence and regularity of distributional solutions

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Bibliographic Details
Main Authors:	Boccardo, Lucio (Author), Croce, Gisella (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] De Gruyter 2014
Series:	De Gruyter Studies in Mathematics 55
Subjects:	Elliptische Differentialgleichung
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	IX, 192 S.
ISBN:	9783110315400 9783110315431

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MARC


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adam_text	CONTENTS NOTATIONS X 1 INTRODUCTION 1 PART I 2 SOME FIXED POINT THEOREMS 5 2.1 INTRODUCTION 5 2.2 BANACH-CACCIOPPOLI THEOREM 5 2.3 BROUWER'S THEOREM 6 2.4 SCHAUDER'S THEOREM10 3 PRELIMINARIES OF REAL ANALYSIS 13 3.1 INTRODUCTION 13 3.2 NEMITSKI'S COMPOSITION THEOREM* 13 3.3 MARCINKIEWICZ SPACES 18 3.4 APPENDIX 22 4 LINEAR AND SEMILINEAR ELLIPTIC EQUATIONS 24 4.1 INTRODUCTION 24 4.2 THE LAX-MILGRAM AND STAMPACCHIA'S THEOREMS 4.3 LINEAR EQUATIONS 27 4.4 SOME SEMILINEAR MONOTONE EQUATIONS 28 4.5 SUB AND SUPERSOLUTIONS METHOD 31 4.6 APPENDIX 34 5 NONLINEAR ELLIPTIC EQUATIONS 37 5.1 INTRODUCTION 37 5.2 SURJECTIVITY THEOREM 37 5.3 THE LERAY-LIONS EXISTENCE THEOREM 40 6 SUMMABILITY OF THE SOLUTIONS 47 6.1 INTRODUCTION 47 6.2 PRELIMINARIES 48 6.3 SOURCES IN LEBESGUE SPACES 51 6.4 SOURCES IN MARCINKIEWICZ SPACES 56 6.5 SOURCES IN DIVERGENCE FORM 58 HTTP://D-NB.INFO/1036475042 VIII * CONTENTS 7 H 2 REGULARITY FOR LINEAR PROBLEMS 61 7.1 INTRODUCTION 61 7.2 PRELIMINARIES 61 7.3 H 2 (D.) REGULARITY OF THE SOLUTIONS 63 8 SPECTRAL ANALYSIS FOR LINEAR OPERATORS 67 8.1 INTRODUCTION 67 8.2 EIGENVALUES OF LINEAR ELLIPTIC OPERATORS 67 8.3 APPLICATIONS TO SOME SEMILINEAR EQUATIONS 74 8.4 APPENDIX 82 9 CALCULUS OF VARIATIONS AND EULER'S EQUATION * 84 9.1 INTRODUCTION 84 9.2 DIRECT METHODS IN THE CALCULUS OF VARIATIONS 84 9.3 EULER EQUATION 86 9.4 SUMMABILITY OF MINIMIZERS OF INTEGRAL FUNCTIONALS 90 9.5 THE EKELAND VARIATIONAL PRINCIPLE 95 9.6 APPENDIX 102 PART II 10 NATURAL GROWTH PROBLEMS 105 10.1 INTRODUCTION 105 10.2 A PROBLEM WITH BOUNDED SOLUTIONS 106 10.3 A PROBLEM WITH UNBOUNDED SOLUTIONS * 112 11 PROBLEMS WITH LOW SUMMABLE SOURCES * 121 11.1 INTRODUCTION 121 11.2 A PRIORI ESTIMATES 123 11.3 DISTRIBUTIONAL SOLUTIONS 130 11.4 THE LINEAR CASE: A DIFFERENT PROOF 130 11.5 ENTROPY SOLUTIONS 132 11.6 A COMPARISON BETWEEN ENTROPY SOLUTIONS AND DISTRIBUTIONAL SOLUTIONS 137 11.7 MEASURE SOURCES 138 11.8 THE REGULARIZING EFFECTS OF A LOWER ORDER TERM* 140 11.9 T-MINIMA 143 11.10 APPENDIX 148 12 UNIQUENESS 150 12.1 INTRODUCTION 150 12.2 MONOTONE ELLIPTIC OPERATORS 150 12.3 A NONMONOTONE ELLIPTIC OPERATOR* 152 12.4 A UNIQUENESS RESULT FOR MEASURE SOURCES 154 13 A PROBLEM WITH POLYNOMIAL GROWTH * 157 13.1 INTRODUCTION 157 13.2 EXISTENCE RESULTS 158 14 A PROBLEM WITH DEGENERATE COERCIVITY 166 14.1 INTRODUCTION 166 14.2 THE CASE 0 8 1 167 14.3 THE CASE 9 1: EXISTENCE AND NONEXISTENCE* 172 14.4 THE REGULARIZING EFFECTS OF A LOWER ORDER TERM 175 BIBLIOGRAPHY 187 INDEX 191
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author	Boccardo, Lucio Croce, Gisella
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physical	IX, 192 S.
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series	De Gruyter Studies in Mathematics
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spelling	Boccardo, Lucio Verfasser (DE-588)1046952323 aut Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce Berlin [u.a.] De Gruyter 2014 IX, 192 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics 55 Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Croce, Gisella Verfasser (DE-588)1046952730 aut Erscheint auch als Online-Ausgabe 978-3-11-031542-4 De Gruyter Studies in Mathematics 55 (DE-604)BV000005407 55 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4372578&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026818273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Boccardo, Lucio Croce, Gisella Elliptic partial differential equations existence and regularity of distributional solutions De Gruyter Studies in Mathematics Elliptische Differentialgleichung (DE-588)4014485-9 gnd
subject_GND	(DE-588)4014485-9
title	Elliptic partial differential equations existence and regularity of distributional solutions
title_auth	Elliptic partial differential equations existence and regularity of distributional solutions
title_exact_search	Elliptic partial differential equations existence and regularity of distributional solutions
title_full	Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce
title_fullStr	Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce
title_full_unstemmed	Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce
title_short	Elliptic partial differential equations
title_sort	elliptic partial differential equations existence and regularity of distributional solutions
title_sub	existence and regularity of distributional solutions
topic	Elliptische Differentialgleichung (DE-588)4014485-9 gnd
topic_facet	Elliptische Differentialgleichung
url	http://deposit.dnb.de/cgi-bin/dokserv?id=4372578&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026818273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT boccardolucio ellipticpartialdifferentialequationsexistenceandregularityofdistributionalsolutions AT crocegisella ellipticpartialdifferentialequationsexistenceandregularityofdistributionalsolutions

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