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Maugeri A., Palagachev D., Softova L.G. — Elliptic and parabolic equations with discontinuous coefficients
Maugeri A., Palagachev D., Softova L.G. — Elliptic and parabolic equations with discontinuous coefficients

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Название: Elliptic and parabolic equations with discontinuous coefficients

Авторы: Maugeri A., Palagachev D., Softova L.G.

Аннотация:

This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research.

Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.


Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 256

Добавлена в каталог: 13.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
${K}_{\Omega}$ property      23 221
${\gamma}_{f}(r)$      106
(${A}^{2*}$) condition      190
(${A}^{2}$) condition      178 183
(${A}^{2}$) condition, vectorial      182
(${A}_{p}$) condition      191
(A) condition      177
Aleksandrov — Bakel'man — Pucci maximum principle      238f
Basic operators, elliptic      210
Basic operators, parabolic      223
BMO      24 105 113
Caccioppoli type estimates      25 63 207 223f
Calderon — Zygmund inequality      39
Calderon — Zygmund kernel      108f
Calderon — Zygmund kernel, parabolic      114
Calderon — Zygmund kernel, variable      114
Campanato space      24 107 221
Caratheodory condition      13 177
Cauchy — Dirichlet problem      57 83 115
Cauchy — Neumann problem      83 153
Commutator      109fT. 114
Conormal derivative problem      36 82
Controlled growth      210
Cordes condition      12f
Cordes condition, elliptic      12 20 68
Cordes condition, for systems      69
Cordes condition, nonlinear      181
Cordes condition, parabolic      58
Differential operator, elliptic      11
Differential operator, parabolic      57 154
Differential operator, strictly elliptic      11
Differential operator, uniformly elliptic      11
Dini continuity      108
Elliptic regularization      149
Elliptic regularizing property      104 117
Finite order of contact      144
Finite type vector field      144
Fundamental estimates      212ff
Fundamental solution of elliptic operator      122
Fundamental solution of parabolic operator      113
Gagliardo — Nirenberg inequality      236
Gehring — Giaquinta — Modica Lemma      209
Generalized reflection      110 115
Gronwall inequality      236
Infinite type vector field      144
Jensen inequality      236
KMO-modulus of continuity      106
Leray — Schauder fixed point theorem      235
Marcinkiewicz space      39 106
Method of continuity      235
Miranda — Talenti estimate (inequality)      21
Morrey space      24 67 107 221
Natural structure conditions      167
Near operators      183ff
Nemyckii operator      237
Neutral type vector field      143
Oblique derivative problem, regular      104 117 136 155
Oblique derivative problem, singular (degenerate)      104 142
Operator, monotone      186
Operator, near      183ff
Operator, strictly monotone      186
Parabolic boundary      115 238
Poincare inequality      236
Pointwise Hoermander condition      112
Riesz potential      236
Riesz — Schauder theory      100 141
Robin problem      135
Shapiro — Lopatinskii compatibility condition      50 104
Solution, classical      12
Solution, generalized (variational)      11 15
Solution, strong      12 16 116 154
Solution, weak      11 15
Strong monotonicity condition      179
Tangency set      142
Tangential gradient      41
VMO      24 106 114
Volume potential      113
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