Regularity of free boundaries in obstacle-type problems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2012
|
| Series: | Graduate studies in mathematics
136 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 221 S. graph. Darst. |
| ISBN: | 9780821887943 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV040384211 | ||
| 003 | DE-604 | ||
| 005 | 20210118 | ||
| 007 | t | ||
| 008 | 120823s2012 xxud||| |||| 00||| eng d | ||
| 010 | |a 2012010200 | ||
| 020 | |a 9780821887943 |c alk. paper |9 978-0-8218-8794-3 | ||
| 035 | |a (OCoLC)809171933 | ||
| 035 | |a (DE-599)BVBBV040384211 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-188 |a DE-384 |a DE-355 |a DE-19 |a DE-11 | ||
| 050 | 0 | |a QA379 | |
| 082 | 0 | |a 515/.353 | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 100 | 1 | |a Petrosyan, Arshak |d 1975- |e Verfasser |0 (DE-588)1025494997 |4 aut | |
| 245 | 1 | 0 | |a Regularity of free boundaries in obstacle-type problems |c Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2012 | |
| 300 | |a X, 221 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 136 | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 7 | |a Partial differential equations -- Miscellaneous topics -- Free boundary problems |2 msc | |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Freies Randwertproblem |0 (DE-588)4155303-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Freies Randwertproblem |0 (DE-588)4155303-2 |D s |
| 689 | 0 | 1 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Shahgholian, Henrik |d 1960- |e Verfasser |0 (DE-588)1027130666 |4 aut | |
| 700 | 1 | |a Ural'ceva, Nina N. |d 1934- |e Verfasser |0 (DE-588)141875305 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-0-8218-8991-6 |
| 830 | 0 | |a Graduate studies in mathematics |v 136 |w (DE-604)BV009739289 |9 136 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025237673 | ||
Record in the Search Index
| _version_ | 1804149427447791616 |
|---|---|
| adam_text | Contents
Preface
ix
Introduction
; 1
Suggestions
for reading/teaching
5
Chapter
1.
Model problems
7
§1.1.
Catalog of problems
7
§1.2.
Model Problems
А, В, С
.
15
§1.3.
W2 p regularity of solutions
17
Notes
22
Exercises
24
Chapter
2.
Optimal regularity of solutions
; 29
§2.1.
Optimal regularity in the classical obstacle problem
■ 29
§2.2.
ACF monotonicity formula and generalizations
32
§2.3.
Optimal regularity in obstacle-type problems
) 42
§2.4.
Optimal regularity up to the fixed boundary
; 45
§2.5.
A counterexample (
49
Notes
51
Exercises
■: 53
Chapters. Preliminary analysis of the free boundary
·. ■. 57
§3.1.
Nondegeneracy
; ; 57
§3.2.
Lebesgue and Hausdorff measures of the free boundary
ş
61
§3.3.
Classes of solutions, rescalings, and blowups
65
vi
Contents
§3.4.
Blowups
68
§3.5.
Weiss-type
monotonicity
formulas
74
Notes
78
Exercises
79
Chapter
4.
Regularity of the free boundary: first results
81
§4.1.
Problem A: C1 regularity of the free boundary near regular
points
81
§4.2.
Problem B: the local structure of the patches
87
§4.3.
Problems A and B: higher regularity of the free boundary
91
§4.4.
Problem C: the free boundary near the branch points
92
§4.5.
Problem C: real analyticity of
Г*
95
Notes
96
Exercises
97
Chapter
5.
Global solutions
99
§5.1.
Classical obstacle problem
100
§5.2.
Problems
А, В
101
§5.3.
Problem
С
108
§5.4.
Approximation by global solutions
109
Notes
112
Exercises
112
Chapter
6.
Regularity of the free boundary: uniform results
115
§6.1.
Lipschitz regularity of the free boundary
115
§6.2.
Cl a Regularity of the free boundary: Problems A and
В
120
§6.3.
С1
regularity of the free boundary: Problem
С
124
§6.4.
Higher regularity: Problems A and
В
128
Notes
131
Exercises
132
Chapter
7.
The singular set
133
§7.1.
The characterization of the singular set
133
§7.2.
Polynomial solutions
135
§7.3.
Examples of singularities
136
§7.4.
Singular set: classical obstacle problem
138
§7.5.
Singular set: Problem A
143
Notes
149
Contents
vii
Exercises
149
Chapter
8.
Touch with the fixed boundary
153
§8.1.
Contact points
153
§8.2.
Global solutions in half-spaces
155
§8.3.
Behavior of the free boundary near the fixed boundary
159
§8.4.
Uniqueness of blowups at contact points
162
Notes
164
Exercises
165
Chapter
9.
The thin obstacle problem
167
§9.1.
The thin obstacle problem
167
§9.2.
C1 regularity
171
§9.3.
Almgren s frequency formula
173
§9.4.
Rescalings and blowups
176
§9.5.
Optimal regularity
181
§9.6.
The regular set
183
§9.7.
The singular set
186
§9.8.
Weiss- and Monneau-type
monotonicity
formulas
188
§9.9.
The structure of the singular set
192
Notes
196
Exercises
197
Bibliography
201
Notation
211
Basic notation
211
Function spaces
212
Notation related to free boundaries
214
Index
217
|
| any_adam_object | 1 |
| author | Petrosyan, Arshak 1975- Shahgholian, Henrik 1960- Ural'ceva, Nina N. 1934- |
| author_GND | (DE-588)1025494997 (DE-588)1027130666 (DE-588)141875305 |
| author_facet | Petrosyan, Arshak 1975- Shahgholian, Henrik 1960- Ural'ceva, Nina N. 1934- |
| author_role | aut aut aut |
| author_sort | Petrosyan, Arshak 1975- |
| author_variant | a p ap h s hs n n u nn nnu |
| building | Verbundindex |
| bvnumber | BV040384211 |
| callnumber-first | Q - Science |
| callnumber-label | QA379 |
| callnumber-raw | QA379 |
| callnumber-search | QA379 |
| callnumber-sort | QA 3379 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)809171933 (DE-599)BVBBV040384211 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02071nam a2200469 cb4500</leader><controlfield tag="001">BV040384211</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210118 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">120823s2012 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2012010200</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821887943</subfield><subfield code="c">alk. paper</subfield><subfield code="9">978-0-8218-8794-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)809171933</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV040384211</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA379</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.353</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 540</subfield><subfield code="0">(DE-625)143245:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Petrosyan, Arshak</subfield><subfield code="d">1975-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1025494997</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Regularity of free boundaries in obstacle-type problems</subfield><subfield code="c">Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 221 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">136</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Boundary value problems</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Partial differential equations -- Miscellaneous topics -- Free boundary problems</subfield><subfield code="2">msc</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Freies Randwertproblem</subfield><subfield code="0">(DE-588)4155303-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Freies Randwertproblem</subfield><subfield code="0">(DE-588)4155303-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Shahgholian, Henrik</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1027130666</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ural'ceva, Nina N.</subfield><subfield code="d">1934-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)141875305</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-0-8218-8991-6</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate studies in mathematics</subfield><subfield code="v">136</subfield><subfield code="w">(DE-604)BV009739289</subfield><subfield code="9">136</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-025237673</subfield></datafield></record></collection> |
| id | DE-604.BV040384211 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:22:51Z |
| institution | BVB |
| isbn | 9780821887943 |
| language | English |
| lccn | 2012010200 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025237673 |
| oclc_num | 809171933 |
| open_access_boolean | |
| owner | DE-188 DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-188 DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-11 |
| physical | X, 221 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Petrosyan, Arshak 1975- Verfasser (DE-588)1025494997 aut Regularity of free boundaries in obstacle-type problems Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva Providence, RI American Mathematical Society 2012 X, 221 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 136 Boundary value problems Partial differential equations -- Miscellaneous topics -- Free boundary problems msc Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Freies Randwertproblem (DE-588)4155303-2 gnd rswk-swf Freies Randwertproblem (DE-588)4155303-2 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Shahgholian, Henrik 1960- Verfasser (DE-588)1027130666 aut Ural'ceva, Nina N. 1934- Verfasser (DE-588)141875305 aut Erscheint auch als Online-Ausgabe 978-0-8218-8991-6 Graduate studies in mathematics 136 (DE-604)BV009739289 136 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrosyan, Arshak 1975- Shahgholian, Henrik 1960- Ural'ceva, Nina N. 1934- Regularity of free boundaries in obstacle-type problems Graduate studies in mathematics Boundary value problems Partial differential equations -- Miscellaneous topics -- Free boundary problems msc Partielle Differentialgleichung (DE-588)4044779-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4155303-2 |
| title | Regularity of free boundaries in obstacle-type problems |
| title_auth | Regularity of free boundaries in obstacle-type problems |
| title_exact_search | Regularity of free boundaries in obstacle-type problems |
| title_full | Regularity of free boundaries in obstacle-type problems Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva |
| title_fullStr | Regularity of free boundaries in obstacle-type problems Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva |
| title_full_unstemmed | Regularity of free boundaries in obstacle-type problems Arshak Petrosyan ; Henrik Shahgholian ; Nina Uraltseva |
| title_short | Regularity of free boundaries in obstacle-type problems |
| title_sort | regularity of free boundaries in obstacle type problems |
| topic | Boundary value problems Partial differential equations -- Miscellaneous topics -- Free boundary problems msc Partielle Differentialgleichung (DE-588)4044779-0 gnd Freies Randwertproblem (DE-588)4155303-2 gnd |
| topic_facet | Boundary value problems Partial differential equations -- Miscellaneous topics -- Free boundary problems Partielle Differentialgleichung Freies Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025237673&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT petrosyanarshak regularityoffreeboundariesinobstacletypeproblems AT shahgholianhenrik regularityoffreeboundariesinobstacletypeproblems AT uralcevaninan regularityoffreeboundariesinobstacletypeproblems |