Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence ; Rhode Island
American Mathematical Society
1984
|
| Schriftenreihe: | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics
160 = 1984,1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Russischen übersetzt |
| Beschreibung: | xi, 287 Seiten |
| ISBN: | 0821830805 |
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| 240 | 1 | 0 | |a Kvazilinejnye vyroždajuščiesja i neravnomerno elliptičeskie uravnenija vtorogo porjadka |
| 245 | 1 | 0 | |a Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| 264 | 1 | |a Providence ; Rhode Island |b American Mathematical Society |c 1984 | |
| 300 | |a xi, 287 Seiten | ||
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| 490 | 1 | |a Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |v 160 = 1984,1 | |
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| 650 | 4 | |a Équations différentielles elliptiques - Solutions numériques | |
| 650 | 4 | |a Équations différentielles paraboliques - Solutions numériques | |
| 650 | 4 | |a Boundary value problems |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Elliptic |x Numerical solutions | |
| 650 | 4 | |a Differential equations, Parabolic |x Numerical solutions | |
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Datensatz im Suchindex
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|---|---|
| adam_text | PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
IN THE ACADEMY OF SCIENCES OF THE USSR
TABLE OF CONTENTS
Preface 1
Basic Notation 3
PART I. QUASILINEAR, NONUNIFORMLY ELLIPTIC AND PARA¬
BOLIC EQUATIONS OF NONDIVERGENCE TYPE 7
CHAPTER 1. The Dirichlet Problem for Quasilinear, Nonuniformly
Elliptic Equations 13
§1. The basic characteristics of a quasilinear elliptic equation 13
§2. A conditional existence theorem 15
§3. Some facts about the barrier technique 16
§4. Estimates of |Vu| on the boundary dU by means of global
barriers 18
§5. Estimates of |Vu| on the boundary by means of local barriers. 22
§6. Estimates of maxn|Vu| for equations with structure described
in terms of the majorant £ 27
§7. The estimate of maxn| Vu| for equations with structure described
in terms of the majorant £2 31
§8. The estimate of maxn| Vu| for a special class of equations 34
§9. The existence theorem for a solution of the Dirichlet problem
in the case of an arbitrary domain Q with a sufficiently smooth
boundary 38
§10. Existence theorem for a solution of the Dirichlet problem in the
case of a strictly convex domain fi 40
CHAPTER 2. The First Boundary Value Problem for Quasilinear,
Nonuniformly Parabolic Equations 43
§1. A conditional existence theorem 43
§2. Estimates of |Vu| on T 46
§3. Estimates of max^lVu| 49
§4. Existence theorems for a classical solution of the first boundary
value problem 54
§5. Nonexistence theorems 56
iii
iv CONTENTS
CHAPTER 3. Local Estimates of the Gradients of Solutions of Quasi
linear Elliptic Equations and Theorems of Liouville Type 60
§1. Estimates of | Vu(io)| in terms of max^(xo)|w| 60
§2. An estimate of |Vu(xo)| in terms of max.Kp(x0)u (min^(io)u)
Harnack s inequality 67
§3. Two sided Liouville theorems 71
§4. One sided Liouville theorems 74
PART H. QUASILINEAR {A,b) ELLIPTIC EQUATIONS 77
CHAPTER 4. Some Analytic Tools Used in the Investigation of Solv¬
ability of Boundary Value Problems for {A,b) Elliptic Equations.... 85
§1. Generalized A derivatives 85
§2. Generalized limit values of a function on the boundary of a
domain 89
§3. The regular and singular parts of the boundary 3(7 95
§4. Some imbedding theorems 98
§5. Some imbedding theorems for functions depending on time 102
§6. General operator equations in a Banach space 106
§7. A special space of functions of scalar argument with values in a
Banach space 112
CHAPTER 5. The General Boundary Value Problem for {A,b,m,m)
Elliptic Equations 118
§1. The structure of the equations and the classical formulation of
the general boundary value problem 118
§2. The basic function spaces and the operators connected with
the general boundary value problem for an (A, b, to, m) elliptic
equation 128
§3. A generalized formulation of the general boundary value prob¬
lem for (A, b, m, m) elliptic equations 137
§4. Conditions for existence and uniqueness of a generalized solution
of the general boundary value problem 139
§5. Linear (A, b) elliptic equations 146
CHAPTER 6. Existence Theorems for Regular Generalized Solutions
of the First Boundary Value Problem for {A, b) Elliptic Equations. 149
§1. Nondivergence (A, b) elliptic equations 149
§2. Existence and uniqueness of regular generalized solutions of the
first boundary value problem 152
§3. The existence of regular generalized solutions of the first bound¬
ary value problem which are bounded in fi together with their
partial derivatives of first order 163
CONTENTS V
PART HI. (A, O) ELLIPTIC AND (A, 0) PARABOLIC EQUATIONS 173
CHAPTER 7. (A, O) Elliptic Equations 177
§ 1. The general boundary value problem for (A, 0, m, m) elliptic equa¬
tions 177
§2. (A, 0) elliptic equations with weak degeneracy 179
§3. Existence and uniqueness of A regular generalized solutions of
the first boundary value problem for (A, 0) elliptic equations... 191
CHAPTER 8. (A, 0) Parabolic Equations 203
§1. The basic function spaces connected with the general boundary
value problem for (A, 0, m, m) parabolic equations 203
§2. The general boundary value problem for (A, 0, m, m) parabolic
equations 216
§3. (A, 0) parabolic equations with weak degeneracy 222
§4. Linear A parabolic equations with weak degeneracy 238
PART IV. ON REGULARITY OF GENERALIZED SOLUTIONS
OF QUASILINEAR DEGENERATE PARABOLIC EQUATIONS. 243
CHAPTER 9. Investigation of the Properties of Generalized Solutions 245
§1. The structure of the equations and their generalized solutions. 245
§2. On regularity of generalized solutions in the variable t 250
§3. The energy inequality 253
§4. Functions of generalized solutions 255
§5. Local estimates in L?m 262
§6. Global estimates in W v° 268
§7. Exponential summability of generalized solutions 270
§8. Local boundedness of generalized solutions 272
§9. Boundedness of generalized solutions of the boundary value prob¬
lem 275
§10. The maximum principle 277
Bibliography 281
|
| any_adam_object | 1 |
| author | Ivanov, A. V. |
| author_facet | Ivanov, A. V. |
| author_role | aut |
| author_sort | Ivanov, A. V. |
| author_variant | a v i av avi |
| building | Verbundindex |
| bvnumber | BV003457194 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 |
| callnumber-raw | QA1 |
| callnumber-search | QA1 |
| callnumber-sort | QA 11 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 700 SK 560 |
| ctrlnum | (OCoLC)243432176 (DE-599)BVBBV003457194 |
| dewey-full | 515.3/53 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515.3/53 510 |
| dewey-search | 515.3/53 510 |
| dewey-sort | 3515.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003457194 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:00:13Z |
| institution | BVB |
| isbn | 0821830805 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002188968 |
| oclc_num | 243432176 |
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| owner | DE-384 DE-12 DE-703 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-188 DE-83 |
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| physical | xi, 287 Seiten |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| series2 | Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics |
| spelling | Ivanov, A. V. aut Kvazilinejnye vyroždajuščiesja i neravnomerno elliptičeskie uravnenija vtorogo porjadka Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order Providence ; Rhode Island American Mathematical Society 1984 xi, 287 Seiten txt rdacontent n rdamedia nc rdacarrier Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 160 = 1984,1 Aus dem Russischen übersetzt Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Équations différentielles paraboliques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Differential equations, Parabolic Numerical solutions Elliptisch entartete Differentialgleichung (DE-588)4152026-9 gnd rswk-swf Parabolisch entartete Differentialgleichung (DE-588)4173244-3 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Parabolische Differentialgleichung (DE-588)4173245-5 gnd rswk-swf Elliptisch entartete Differentialgleichung (DE-588)4152026-9 s DE-604 Parabolisch entartete Differentialgleichung (DE-588)4173244-3 s Elliptische Differentialgleichung (DE-588)4014485-9 s Randwertproblem (DE-588)4048395-2 s Parabolische Differentialgleichung (DE-588)4173245-5 s Numerisches Verfahren (DE-588)4128130-5 s Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics 160 = 1984,1 (DE-604)BV000009943 160 = 1984,1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002188968&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivanov, A. V. Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order Matematičeskij Institut Imeni V. A. Steklova <Moskva>: Proceedings of the Steklov Institute of Mathematics Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Équations différentielles paraboliques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Differential equations, Parabolic Numerical solutions Elliptisch entartete Differentialgleichung (DE-588)4152026-9 gnd Parabolisch entartete Differentialgleichung (DE-588)4173244-3 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| subject_GND | (DE-588)4152026-9 (DE-588)4173244-3 (DE-588)4014485-9 (DE-588)4128130-5 (DE-588)4048395-2 (DE-588)4173245-5 |
| title | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_alt | Kvazilinejnye vyroždajuščiesja i neravnomerno elliptičeskie uravnenija vtorogo porjadka |
| title_auth | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_exact_search | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_full | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_fullStr | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_full_unstemmed | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_short | Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| title_sort | quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order |
| topic | Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Équations différentielles paraboliques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Differential equations, Parabolic Numerical solutions Elliptisch entartete Differentialgleichung (DE-588)4152026-9 gnd Parabolisch entartete Differentialgleichung (DE-588)4173244-3 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Randwertproblem (DE-588)4048395-2 gnd Parabolische Differentialgleichung (DE-588)4173245-5 gnd |
| topic_facet | Problèmes aux limites - Solutions numériques Équations différentielles elliptiques - Solutions numériques Équations différentielles paraboliques - Solutions numériques Boundary value problems Numerical solutions Differential equations, Elliptic Numerical solutions Differential equations, Parabolic Numerical solutions Elliptisch entartete Differentialgleichung Parabolisch entartete Differentialgleichung Elliptische Differentialgleichung Numerisches Verfahren Randwertproblem Parabolische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002188968&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000009943 |
| work_keys_str_mv | AT ivanovav kvazilinejnyevyrozdajusciesjaineravnomernoellipticeskieuravnenijavtorogoporjadka AT ivanovav quasilineardegenerateandnonuniformlyellipticandparabolicequationsofsecondorder |