Schulz F., Dold A. (Ed), Eckmann B. (Ed) — Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampere Equations in Two Dimensions :: Электронная библиотека попечительского совета мехмата МГУ

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Schulz F., Dold A. (Ed), Eckmann B. (Ed) — Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampere Equations in Two Dimensions

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Название: Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampere Equations in Two Dimensions

Авторы: Schulz F., Dold A. (Ed), Eckmann B. (Ed)

Аннотация:

These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère equations, a theory largely developed by H. Lewy and E. Heinz which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1990

Количество страниц: 123

Добавлена в каталог: 04.07.2008

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Предметный указатель

Absolutely continuous function      1 12
Alexandrov theorem      101
Analytic divisor      49
Analytic function      47 51 52 63
Analyticity      47
Anti -conformal map      62 63
Approximation      1 2 31 32 70 103 111
Approximation Lemma      75
Area element      107
Asymptotic expansion      74 83 89
Ball of radius R centered at x      2
Banach space      1
Beltrami system      62 63—65 70 102
Bi — Lipschitz map      30
Binary elliptic system      53
Borel measurable function      85
Caccioppoli inequality      15 16 18
Campanato criterion      38
Campanato technique      15 37
Canonical form      61
Carleman — Hartman — Wintnertheorem      75
Carleman's integral estimates      72
Cauchy principle value      43
Cauchy type integral      45
Cauchy — Kovalevsky theorem      66
Cauchy — Riemann system      40 46 63
Cauchy — Riemann — Beltrami system      62
Characteristic form      28 94 96 102
Characteristic parameters      94 96
Christoffel symbol      106
Codazzi — Mainardi equations      107 111
Coefficientsl      5 21 23 35 70 71 80 85 86 95 107 111
Complex notation      39
Conformal map      62 63 82
Conformality relations      62 64 70 71 80 96 97 103 110—112
Continuity modulus      11
Convex function      109
Convex surface      101 108
Convexity      28 29
Coordinate change      63 66 67
Counterexample      104
Courant — Lebesgue lemma      11 27 55 58 69 93 114
Cramer's rule      59 110
Curvature      106
Darboux equation      109 110
Darboux system      110
De Giorgi lemma      7
Diffeomorphism      70 80 94
Difference quotient method      16
Differential form      68 80 111
Differential inequality      47 54 56 57 72 75 81 83 87 90
Dilation constant      36
Dilation estimate(s)      30 100 114
Dirichlet growth      2 3 5
Dirichlet integral      11 98 113 114
Dirichlet problem      18
Discriminant      28 34
Divergence structure      15 33
Divergence theorem      32 39 97
Elliptic equation(s)      15 18 21 72 94
Elliptic inequality      80 81 82
Elliptic system      53 56 65 67 69 99
Ellipticity      28 29 36 95
Equicontinuous maps      69 93
Error estimate      37
Essential supremum      1
Estimate      18 34 45 48 54 58 92 97 98 101 108 112 113
First fundamental form      106
Freezing coefficients      21
Function theory      72
GauB curvature      101 107 108 109
GauB curvature equation      108
GauB equations      106 107 109 110 114
GauB — Green theorem      41 43 72
GauB — Weingarten equations      107
Graph      107 109
Hadamard' s integral estimates      39
Harmonic function      51 52
Harnack inequality      50 51
Hartman—Wintner theorem      72
Heinz estimates      100
Heinz — Lewy counterexample      104
Heinz — Lewy system      55 85
Holder continuity      37 38
Holder continuous function      2 5 21 23 48
Holder continuous map      70
Holder estimate      100
Holder norm      2
Holder space (class)      5 21 70

Homeomorphism      11 13 27 39 54 58 66 67 71 89 92 95 98 101 110
Homotopy invariance      84
In the large      61
In the small      61
Index (of a curve)      89
Induction      73 77
Initial value problem      104
Integrability condition(s)      62 66 69 70 107 111
Iteration (lemma)      20 37
Jacobian      30 53 69 92
Jordan curve      89
Lagrange identity      106
Laplace operator      39
Lebesgue Differentiation Theorem      5 11
Legendre like transformation      30 33 100
Line segment      101
Linear equation      27
Linear system      90
Linear theory      34
Lipschitz continuity      30
Lipschitz continuous function      1 85 98 99
Lipschitz map      30
Local behavior      72
Local coordinates      66
Locally convex surface      109 110 112 113
Logarithmic difference      49
Mapping      97
Maximum principle      25
Mean curvature      107 112
Metric      65
Minimizing sequence      8
Monge — Ampere equation      9 30 33—35 70 94—101 104
Monotonicity      20
Multiindex      1
Neighborhood      61
New independent variables      94
normal      106
Normalization      80 81
Orthogonal matrix      86
Oscillation integral      5
Partial fractions decomposition      44—46 74
Poincare inequality      4 5 10 11 18 19 22 25
Polar coordinates      12
Polynomial      7 8 10 11
Precise representative      1
Pseudoanalytic function      47 49 50
Quasilinear system      15 23 27 39
Radius vector      106 108—110 112—114
Real analytic function      65
Real analytic map      66
Regular surface      106 109
Regularity      15—17 34 107 110
Regularity theory      69 70 95
Representation      41 48 49 51
Riemann surface      67
Riemannian metric      61 66
Scaling      18
Second derivative estimates      100 104
Second fundamental form      106
Similarity principle      49 51 72
Singular integral      43 45
Singularity      47
Sobolev embedding theorem      17
Sobolev function      1 2
Sobolev inequality      10 11 17
Sobolev Norm      1
Sobolev space      1
Structural condition      104
System (linear)      90 91
Theorema egregium      107 111
Topological lemma      89
Transformation      30 33 36 63 66 67 100
Uniform ellipticity      28 29 30
Uniformization theorem      67
Uniformizer      67 70 71
Uniformizing parameters      61 62 63 66
Unique continuation principle      81 83
Unit normal      106
Univalent mapping      53 55 65 90
Variable transformation      36
Variational problem      8
Weak compactness      17 70
Weak derivative      17
Weak partial derivative      1
Weak solution      15 17 31 32 42
WeierstraC approximation theorem      68
Weingarten equations      107
Winding number      84
Wirtinger operator      39

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