Theorems on regularity and singularity of energy minimizing maps: based on lecture notes by Norbert Hungerbühler
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1996
|
| Schriftenreihe: | Lectures in mathematics / ETH Zürich
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 152 S. graph. Darst. |
| ISBN: | 376435397X 081765397X |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010620347 | ||
| 003 | DE-604 | ||
| 005 | 20220117 | ||
| 007 | t | ||
| 008 | 960212s1996 gw d||| |||| 00||| eng d | ||
| 016 | 7 | |a 946676038 |2 DE-101 | |
| 020 | |a 376435397X |c (Basel ...) kart. : ca. DM 44.00, ca. S 321.00, sfr 38.00 |9 3-7643-5397-X | ||
| 020 | |a 081765397X |c (Boston) kart. |9 0-8176-5397-X | ||
| 035 | |a (OCoLC)34318331 | ||
| 035 | |a (DE-599)BVBBV010620347 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c DE | ||
| 049 | |a DE-355 |a DE-824 |a DE-12 |a DE-29T |a DE-19 |a DE-384 |a DE-634 |a DE-739 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA614.58 | |
| 082 | 0 | |a 515/.352 |2 20 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 100 | 1 | |a Simon, Leon |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Theorems on regularity and singularity of energy minimizing maps |b based on lecture notes by Norbert Hungerbühler |c Leon Simon |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a VII, 152 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Lectures in mathematics / ETH Zürich | |
| 650 | 7 | |a Applications différentiables |2 ram | |
| 650 | 7 | |a Applications harmoniques |2 ram | |
| 650 | 7 | |a Singularités (Mathématiques) |2 ram | |
| 650 | 4 | |a Differentiable mappings | |
| 650 | 4 | |a Harmonic maps | |
| 650 | 4 | |a Singularities (Mathematics) | |
| 650 | 0 | 7 | |a Singularität |g Mathematik |0 (DE-588)4077459-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Regularität |0 (DE-588)4049074-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Abbildung |0 (DE-588)4023452-6 |D s |
| 689 | 0 | 1 | |a Regularität |0 (DE-588)4049074-9 |D s |
| 689 | 0 | 2 | |a Singularität |g Mathematik |0 (DE-588)4077459-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007085239 | ||
Datensatz im Suchindex
| _version_ | 1804125095443038208 |
|---|---|
| adam_text | Contents
Preface vii
1 Analytic Preliminaries
1.1 Holder Continuity 1
1.2 Smoothing 1
1.3 Functions with L2 Gradient 5
1.4 Harmonic Functions 8
1.5 Weakly Harmonic Functions 10
1.6 Harmonic Approximation Lemma 10
1.7 Elliptic regularity 11
1.8 A Technical Regularity Lemma 13
2 Regularity Theory for Harmonic Maps
2.1 Definition of Energy Minimizing Maps 19
2.2 The Variational Equations 20
2.3 The e Regularity Theorem 22
2.4 The Monotonicity Formula 23
2.5 The Density Function 24
2.6 A Lemma of Luckhaus 25
2.7 Corollaries of Luckhaus Lemma 26
2.8 Proof of the Reverse Poincarc Inequality 29
2.9 The Compactness Theorem 32
2.10 Corollaries of the ^ Regularity Theorem 35
2.11 Remark on Upper Semicontinuity of the Density BM(y) 37
2.12 Appendix to Chapter 2 37
2.12.1 Absolute Continuity Properties of Functions in Yla 37
2.12.2 Proof of Luckhaus Lemma (Lemma 1 of Section 2.6) 38
2.12.3 Nearest point projection 42
2.12.4 Proof of the e regularity theorem in case n = 2 46
v
vi Contents
3 Approximation Properties of the Singular Set
3.1 Definition of Tangent Map 51
3.2 Properties of Tangent Maps 52
3.3 Properties of Homogeneous Degree Zero Minimizers 52
3.4 Further Properties of singu 54
3.5 Definition of Top dimensional Part of the Singular Set 58
3.6 Homogeneous Degree Zero ip with dim S(ip) = n — 3 58
3.7 The Geometric Picture Near Points of sing»w 59
3.8 Consequences of Uniqueness of Tangent Maps 61
3.9 Approximation properties of subsets of IRn 62
3.10 Uniqueness of Tangent maps with isolated singularities 67
3.11 Functionals on vector bundles 72
3.12 The Liapunov Schmidt Reduction 74
3.13 The Lojasiewicz Inequality for J 78
3.14 Lojasiewicz for the Energy functional on S 1 80
3.15 Proof of Theorem 1 of Section 3.10 82
3.16 Appendix to Chapter 3 87
3.16.1 The Liapunov Schmidt Reduction in a
Finite Dimensional Setting 87
4 Rectifiability of the Singular Set
4.1 Statement of Main Theorems 91
4.2 A general rectifiability lemma 92
4.3 Gap Measures on Subsets of ]Rn 104
4.4 Energy Estimates 110
4.5 L2 estimates 120
4.6 The deviation function %[ 129
4.7 Proof of Theorems 1, 2 of Section 4.1 135
4.8 The case when fi has arbitrary Riemannian metric 143
Bibliography 147
Index 150
|
| any_adam_object | 1 |
| author | Simon, Leon |
| author_facet | Simon, Leon |
| author_role | aut |
| author_sort | Simon, Leon |
| author_variant | l s ls |
| building | Verbundindex |
| bvnumber | BV010620347 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.58 |
| callnumber-search | QA614.58 |
| callnumber-sort | QA 3614.58 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 SK 560 SK 540 |
| ctrlnum | (OCoLC)34318331 (DE-599)BVBBV010620347 |
| dewey-full | 515/.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| 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>02181nam a2200529 c 4500</leader><controlfield tag="001">BV010620347</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220117 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">960212s1996 gw d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">946676038</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">376435397X</subfield><subfield code="c">(Basel ...) kart. : ca. DM 44.00, ca. S 321.00, sfr 38.00</subfield><subfield code="9">3-7643-5397-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">081765397X</subfield><subfield code="c">(Boston) kart.</subfield><subfield code="9">0-8176-5397-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)34318331</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010620347</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA614.58</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.352</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 560</subfield><subfield code="0">(DE-625)143246:</subfield><subfield code="2">rvk</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">Simon, Leon</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Theorems on regularity and singularity of energy minimizing maps</subfield><subfield code="b">based on lecture notes by Norbert Hungerbühler</subfield><subfield code="c">Leon Simon</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Basel [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 152 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="0" ind2=" "><subfield code="a">Lectures in mathematics / ETH Zürich</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Applications différentiables</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Applications harmoniques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Singularités (Mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differentiable mappings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic maps</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Singularities (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Singularität</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4077459-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Regularität</subfield><subfield code="0">(DE-588)4049074-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Harmonische Abbildung</subfield><subfield code="0">(DE-588)4023452-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Regularität</subfield><subfield code="0">(DE-588)4049074-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Singularität</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4077459-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=007085239&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:BVB01-007085239</subfield></datafield></record></collection> |
| id | DE-604.BV010620347 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:06Z |
| institution | BVB |
| isbn | 376435397X 081765397X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007085239 |
| oclc_num | 34318331 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-12 DE-29T DE-19 DE-BY-UBM DE-384 DE-634 DE-739 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-12 DE-29T DE-19 DE-BY-UBM DE-384 DE-634 DE-739 DE-11 DE-188 |
| physical | VII, 152 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Lectures in mathematics / ETH Zürich |
| spelling | Simon, Leon Verfasser aut Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler Leon Simon Basel [u.a.] Birkhäuser 1996 VII, 152 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lectures in mathematics / ETH Zürich Applications différentiables ram Applications harmoniques ram Singularités (Mathématiques) ram Differentiable mappings Harmonic maps Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 gnd rswk-swf Harmonische Abbildung (DE-588)4023452-6 s Regularität (DE-588)4049074-9 s Singularität Mathematik (DE-588)4077459-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simon, Leon Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler Applications différentiables ram Applications harmoniques ram Singularités (Mathématiques) ram Differentiable mappings Harmonic maps Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Regularität (DE-588)4049074-9 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4049074-9 (DE-588)4023452-6 |
| title | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler |
| title_auth | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler |
| title_exact_search | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler |
| title_full | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler Leon Simon |
| title_fullStr | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler Leon Simon |
| title_full_unstemmed | Theorems on regularity and singularity of energy minimizing maps based on lecture notes by Norbert Hungerbühler Leon Simon |
| title_short | Theorems on regularity and singularity of energy minimizing maps |
| title_sort | theorems on regularity and singularity of energy minimizing maps based on lecture notes by norbert hungerbuhler |
| title_sub | based on lecture notes by Norbert Hungerbühler |
| topic | Applications différentiables ram Applications harmoniques ram Singularités (Mathématiques) ram Differentiable mappings Harmonic maps Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Regularität (DE-588)4049074-9 gnd Harmonische Abbildung (DE-588)4023452-6 gnd |
| topic_facet | Applications différentiables Applications harmoniques Singularités (Mathématiques) Differentiable mappings Harmonic maps Singularities (Mathematics) Singularität Mathematik Regularität Harmonische Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007085239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT simonleon theoremsonregularityandsingularityofenergyminimizingmapsbasedonlecturenotesbynorberthungerbuhler |