Nonlinear partial differential equations of second order:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Providence, RI
American Mathemat. Soc.
1991
|
| Series: | Translations of mathematical monographs
95 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Chines. übers. |
| Physical Description: | VII, 251 S. |
| ISBN: | 0821845543 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV005453237 | ||
| 003 | DE-604 | ||
| 005 | 20220217 | ||
| 007 | t | ||
| 008 | 920728s1991 |||| 00||| engod | ||
| 020 | |a 0821845543 |9 0-8218-4554-3 | ||
| 035 | |a (OCoLC)24247762 | ||
| 035 | |a (DE-599)BVBBV005453237 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 1 | |a eng |h chi | |
| 049 | |a DE-12 |a DE-384 |a DE-355 |a DE-29T |a DE-83 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA377 | |
| 082 | 0 | |a 515/.353 |2 20 | |
| 084 | |a SK 540 |0 (DE-625)143245: |2 rvk | ||
| 084 | |a SK 560 |0 (DE-625)143246: |2 rvk | ||
| 084 | |a 35K55 |2 msc | ||
| 100 | 1 | |a Dong, Guangchang |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Fei-xian-xing-er-jie-pian-wei-fen-fang-cheng |
| 245 | 1 | 0 | |a Nonlinear partial differential equations of second order |c Guangchang Dong |
| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 1991 | |
| 300 | |a VII, 251 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 95 | |
| 500 | |a Aus d. Chines. übers. | ||
| 650 | 7 | |a Equations aux dérivées partielles |2 ram | |
| 650 | 7 | |a Equations différentielles non linéaires |2 ram | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Équations différentielles non linéaires | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 0 | 7 | |a Ordnung 2 |0 (DE-588)4350619-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |D s |
| 689 | 0 | 1 | |a Ordnung 2 |0 (DE-588)4350619-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Nichtlineare partielle Differentialgleichung |0 (DE-588)4128900-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 2 | |5 DE-604 | |
| 830 | 0 | |a Translations of mathematical monographs |v 95 |w (DE-604)BV000002394 |9 95 | |
| 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=003411446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003411446 | ||
Record in the Search Index
| _version_ | 1804119663357984768 |
|---|---|
| adam_text | Contents
Introduction 1
Notes for the English Translation 3
CHAPTER I. The First Boundary Value Problem for Second Order
Quasilinear Parabolic Equations with Principal Part in
Divergence Form 7
§ 1. Uniform and Holder estimates for the solution 7
§2. A uniform bound for Dxu 10
§3. A Holder estimate for Dxu 17
§4. Existence and uniqueness of the solution for the first boundary
value problem 23
CHAPTER II. A Periodic Boundary Value Problem for a Nonlinear
Telegraph Equation 31
§ 1. Solvability for higher dimensional telegraph equations in the
nonresonance case 32
§2. A discussion on the resonance case 36
§3. Regularity of a generalized solution 39
CHAPTER III. The Initial Value Problem for a Nonlinear Schrodinger
Equation 43
§ 1. Background materials 43
§2. The initial value problem for the linear Schrodinger equation 45
§3. The initial value problem for a nonlinear Schrodinger equation 48
CHAPTER IV. Multi Dimensional Subsonic Flows Around an
Obstacle 59
§1. Introduction 59
§2. Background material for the linear problem 61
§3. Solution to the auxiliary problem 64
§4. Resolution of the problem of a flow passing an obstacle and
elementary properties of the solution 73
§5. Further properties of the solution 74
V
vi CONTENTS
CHAPTER V. The Initial Boundary Value Problem for Degenerate
Quasilinear Parabolic Equations 77
§1. Formulation of the problem and a Holder estimate for the
solution 78
§2. Solvability for the first boundary value problem 98
§3. Uniqueness of the solution 101
§4. The initial value problem 107
CHAPTER VI. The Speed of Propagation of the Solution of a
Degenerate Quasilinear Parabolic Equation 109
§ 1. An estimate on the domain of dependence 109
§2. A lower estimate for the solution 117
CHAPTER VII. Aleksandrov and Bony Maximum Principles for
Parabolic Equations 121
§1. Introduction 121
§2. Some properties of convex functions 125
§3. Convex envelopes 135
§4. Several Aleksandrov maximum principles 139
§5. Bony maximum principles 145
CHAPTER VIII. The Density Theorem and Its Applications 149
§1. The statement of the density theorem 149
§2. Several lemmas and the proof of the density theorem 151
§3. The Harnack inequality for parabolic equations with
measurable coefficients 158
§4. A Holder estimate for the solution of a quasilinear parabolic
equation 159
§5. A Holder estimate for the solution for a quasilinear parabolic
system 162
CHAPTER IX. Fully Nonlinear Parabolic Equations 169
§ 1. A uniform bound for a solution u and an interior estimate for
Dxu 170
§2. An interior estimate for the second derivatives 174
§3. An interior Holder estimate for the second derivatives 181
§4. A near boundary Holder estimate for u 184
§5. Uniform and Holder estimates for Dxu near the boundary 189
§6. Near boundary uniform and Holder estimates for the second
derivatives 198
§7. Uniqueness and existence of a solution for the first boundary
value problem under the natural structure conditions 200
CONTENTS vii
CHAPTER X. Fully Nonlinear Parabolic Equations (Continued) 207
§ 1. The density theorem for quasilinear parabolic equations with
natural structure condition of the second kind 207
§2. A Holder estimate for the solution and unique solvability for
the first boundary value problem 227
§3. Certain apriori estimates for the solutions of a fully nonlinear
parabolic equation with natural structure condition of the
second kind and the unique solvability of the first boundary
value problem 238
Symbols 245
References 247
|
| any_adam_object | 1 |
| author | Dong, Guangchang |
| author_facet | Dong, Guangchang |
| author_role | aut |
| author_sort | Dong, Guangchang |
| author_variant | g d gd |
| building | Verbundindex |
| bvnumber | BV005453237 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 560 |
| ctrlnum | (OCoLC)24247762 (DE-599)BVBBV005453237 |
| 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>02358nam a2200565 cb4500</leader><controlfield tag="001">BV005453237</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20220217 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">920728s1991 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821845543</subfield><subfield code="9">0-8218-4554-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)24247762</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005453237</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="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">chi</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA377</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.353</subfield><subfield code="2">20</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="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">35K55</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dong, Guangchang</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Fei-xian-xing-er-jie-pian-wei-fen-fang-cheng</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear partial differential equations of second order</subfield><subfield code="c">Guangchang Dong</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathemat. Soc.</subfield><subfield code="c">1991</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 251 S.</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">Translations of mathematical monographs</subfield><subfield code="v">95</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Aus d. Chines. übers.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equations aux dérivées partielles</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Equations différentielles non linéaires</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Équations aux dérivées partielles</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Équations différentielles non linéaires</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Nonlinear</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differential equations, Partial</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ordnung 2</subfield><subfield code="0">(DE-588)4350619-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</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">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Ordnung 2</subfield><subfield code="0">(DE-588)4350619-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Nichtlineare partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4128900-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Partielle Differentialgleichung</subfield><subfield code="0">(DE-588)4044779-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Translations of mathematical monographs</subfield><subfield code="v">95</subfield><subfield code="w">(DE-604)BV000002394</subfield><subfield code="9">95</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=003411446&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:BVB01-003411446</subfield></datafield></record></collection> |
| id | DE-604.BV005453237 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:29:46Z |
| institution | BVB |
| isbn | 0821845543 |
| language | English Chinese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003411446 |
| oclc_num | 24247762 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-355 DE-BY-UBR DE-29T DE-83 DE-11 DE-188 |
| physical | VII, 251 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Dong, Guangchang Verfasser aut Fei-xian-xing-er-jie-pian-wei-fen-fang-cheng Nonlinear partial differential equations of second order Guangchang Dong Providence, RI American Mathemat. Soc. 1991 VII, 251 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 95 Aus d. Chines. übers. Equations aux dérivées partielles ram Equations différentielles non linéaires ram Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Nonlinear Differential equations, Partial Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd rswk-swf Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 s Ordnung 2 (DE-588)4350619-7 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Translations of mathematical monographs 95 (DE-604)BV000002394 95 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003411446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dong, Guangchang Nonlinear partial differential equations of second order Translations of mathematical monographs Equations aux dérivées partielles ram Equations différentielles non linéaires ram Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Nonlinear Differential equations, Partial Ordnung 2 (DE-588)4350619-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| subject_GND | (DE-588)4350619-7 (DE-588)4044779-0 (DE-588)4128900-6 |
| title | Nonlinear partial differential equations of second order |
| title_alt | Fei-xian-xing-er-jie-pian-wei-fen-fang-cheng |
| title_auth | Nonlinear partial differential equations of second order |
| title_exact_search | Nonlinear partial differential equations of second order |
| title_full | Nonlinear partial differential equations of second order Guangchang Dong |
| title_fullStr | Nonlinear partial differential equations of second order Guangchang Dong |
| title_full_unstemmed | Nonlinear partial differential equations of second order Guangchang Dong |
| title_short | Nonlinear partial differential equations of second order |
| title_sort | nonlinear partial differential equations of second order |
| topic | Equations aux dérivées partielles ram Equations différentielles non linéaires ram Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Nonlinear Differential equations, Partial Ordnung 2 (DE-588)4350619-7 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Nichtlineare partielle Differentialgleichung (DE-588)4128900-6 gnd |
| topic_facet | Equations aux dérivées partielles Equations différentielles non linéaires Équations aux dérivées partielles Équations différentielles non linéaires Differential equations, Nonlinear Differential equations, Partial Ordnung 2 Partielle Differentialgleichung Nichtlineare partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003411446&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT dongguangchang feixianxingerjiepianweifenfangcheng AT dongguangchang nonlinearpartialdifferentialequationsofsecondorder |