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Morrey C. — Multiple integrals in the calculus of variations
Morrey C. — Multiple integrals in the calculus of variations



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Название: Multiple integrals in the calculus of variations

Автор: Morrey C.

Аннотация:

From the reviews: "…the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. …The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book."

M. R. Hestenes in Journal of Optimization Theory and Applications

"The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems."

L. Schmetterer in Monatshefte f?r Mathematik

 "The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book."

M. Coroi-Nedeleu in Revue Roumaine de Math?matiques Pures et Appliqu?es



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 506

Добавлена в каталог: 21.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$d(\Gamma), d^*(\Gamma)$      374 380
$l(\Gamma), l^*(\Gamma)$      373 380
$\delta$ cohomology      322
$\delta$-Neumann problem      320
Admissible boundary coordinate system      300
Admissible coordinate system      300
Admissible measure      489
Algebraic boundary b(X, A)      411
Area integral      1
Basis (for complex 1 forms)      331
Basis, orthogonal      332
Boundary b M of M      300
Boundary operator      319
Boundary values      76
Bounded slope condition      98
Calderon — Zygmund inequalities      56 58
Calderon's extension theorem      74
Cauchy inequality      35
Class $\mathfrak{C}$(A, L)      411
Closed forms $\varphi$(d$\varphi = 0$)      299
Coerciveness inequality      253
Complementing condition      212
Complex Dirichlet integral $d(\varphi ,\psi)$      320
Complex improper integral      174
Complex-analytic manifold      317
Contractible      414
Convex function      21
Convex set      21
Cover (in the sence of Vitali)      409
Dini condition      54
Direct methods      16
Dirichlet data      252
Dirichlet growth condition      32
Dirichlet growth lemma      79
Dirichlet integral      1
Dirichlet integral for forms      291 320
Dirichlet's principle      5
Dirtchlet problem      44
Distance $d_0(\Sigma, \Sigma')$      439
Distance between Erechet varieties      351
Distance between mappings [D(z1,z2)]      350
Distance geodesic      378
Distance point set      406
Distribution derivatives      20
Domain $B_{0hR}$      181
Domain $B_{hR}$      174
Domain $G_{hR}$      181
Domain Lipschitz (of class $C_1^0$)      25 77
Domain of class $C^n, C_{\mu}^n, C^{\infty}$, analytic      4
Domain of class $D'$      384
Domain strongly Lipschitz      72
Domain with regular boundary      72
Elementary function      43
Elliptic systems (of differential equations)      210
Euler's equations      2 7 8
Exterior co-differential      290
Exterior derivative      290
Exterior differential r-forms      288
Extremal      32
Federer's convergence property      492
Federer's multiplicity function      480
Field of extremals      14
First differential      31
First variation      7 8
Form, closed      299
Form, closed, $\mathfrak{L}_2$-flat      299
Form, closed, complex, of type (p,q)      318
Form, closed, even      288
Form, closed, exterior differential      288
Form, closed, in $H_p^1$, $\mathfrak{L}_p$      288
Form, closed, normal part of a      301 302
Form, closed, odd      288
Form, potential of a      295 314
Form, tangential part of a      301 302
Frechet variety      351
Frechet variety on a manifold      379
Frechet variety oriented      353
Friedrichs mollifier      20
Function, absolutely continuous in the sense of Tonelli      19 67
Function, admissible      8
Function, essentially homogeneous of degree p      47
Function, mollified      20
Function, monotone in the sense of Lebesgue      16 17
Function, of class $C_{\mu}^n$      4
Function, of class $H_p^2(G)$, $H_n^m(G)$      20
Function, quasi-convex      112
Function, strongly in $H_8^1(\partial R)$      114
Function, strongly quasi-convex      114
Gaffney-garding inequality      293
Garding’s inequality      253
Generalized derivatives      62
Generalized surface      354
Geodesic cones C(P,S), C($\Pi$,S)      409 410
Geodesic k-plane      406
Geodesic k-plane centered at P      406
Gradient, $\nabla z$      1
Green's function      44
Harmonic field      294
Harmonic form      316
Harmonic function      40
Hausdorff outer measure      350 408
Hermitean metric      317
Hilbert transform      55
Hilbert's invariant integral      14
Hoelder condition      4
Hopf's extension theorem      482 483
Inner product, $((\varphi ,\psi), (\varphi ,\psi))_z$      333
Inner product, $D(\varphi ,\psi)$      320
Inner product, localized (of forms)      302
Inner product, of complex forms      319
Inner product, of complex forms, localized      319
Inner product, of forms in $H_2^1$      289
Inner product, of forms in $\mathfrak{L}_2$      2 288
Integral in parametric form      2 349
Integrals over oriented Frechet varieties      353
Integrand, normal      92
Integrand, normal of a parametric problem      349
Integrand, of type I      96
Integrand, of type II      97
Jacobi condition      15
Jacobi's equation      13
Jensen's inequality      21
Kodaira decomposition      286 298 312 322
Laplace's equation      43
Lebesgue area of a Frechet surface      352
Legendre condition      2 10
Legendre — Hadamard condition      11
Linear functionals on $H_p^m(G)$      70
Linear sets $\mathfrak{C,D}$      312
Lipschitz condition      4
Lipschitz convergence      113
Lipschitz domain (of class $C_1^0$)      25
Localized inner product      301
Localized inner product of complex forms      319
Manifold with boundary (of class $C_{\mu}^n$, etc.)      300
Mapping, $r_k: C_k' - C_{N-v-1}'' \rightarrow C_{k-1}'$      453
Mapping, $u_v(y)$      454
Mapping, $\mathfrak{\varrho}_v: R_N - C_{N-v-1}'' \rightarrow R_N$      454
Mapping, abcolutely continious      379 382
Mapping, light      489
Mapping, monotone      489
Mapping, of class $H_p^1$      382
Mapping, of class $\overline{H_p^1}$      379
Maximum principle      40 61
Mean value properties of harmonic functions      40 41
Measurable mappings      378
Minimizing sequences      16
Minimum conditions (on a general elliptic system)      215
Minus potential (of a form)      310
Multinomial coefficient $C_{\alpha}$      63
n-th gradient $\nabla^n z$      4
Norm $'\|u\|_{sR}$      338
Norm $\|u\|_{sR}$      337
Norm $\|\varphi\|_{s}$ for complex forms      342
Normal coordinate system      402
Normal coordinate system centered at a point q on $\mathfrak{R}$      402
Normal part (of a form)      301 302
Operator $Box$, for complex forms      320
Operator $\delta$, for complex forms      319
Operator b, for complex forms      319
Operator L, for complex forms      321
Operator N, for complex forms      321
Order 0[z, $\tau(\partial G)$]      356 357 359 480
Oriented Frechet variety      353
Orthogonal basis      332
Parallel geodesic planes      443
Parametric representation      351
Plus potential (of a form)      310
Poincare’s inequality      69
Point set distance D($S_1$, $S_2$)      406
Poisson’s equation      47
Poisson’s integral formula      45 46
Polyhedral cone      460
Potential      47
Potential of a form      259 314
Principal part (of a differential operator)      210
Problem of Plateau in $R_N$      375 376
Projection $P^I$      485
Projection on a geodesic p-plane      435
Properly elliptic system      211
Quasi-linear equations      8
Quasi-potential      86
Reflection principle      54
Regular mapping      64
Regular parametric problem      32
Regular Variational problem      8 11
Reifenberg cone inequality      459 460
Reifenberg's ($\varepsilon$, R1) condition      433
Rellich's theorem      75
Riemannian manifold of class $C^k, C_{\mu}^k$      288
Root condition      211
Second variation      10
Set (S,$\varrho$)      406
Sets $C_k'(a,\varepsilon)$, $C_k''(a,\varepsilon)$      453
Simplicial cone      460
Singular integrals      50
Slope functions      14
Sobolev lemmas      78 80
Sobolev spaces      19 20
Sobolev’s embedding theorem      80
Space $H_p^m(G)$      20 288
Space $H_{p0}^m(G)$      68
Space $L_p(E,\{mu})$ (of mappings)      378
Space $\mathfrak{A}$      318
Space $\mathfrak{A}_0,\mathfrak{A}^{pq}$      319
Space $\mathfrak{B}_2^{+}$ and $\mathfrak{B}_2^{-}$      378
Space $\mathfrak{B}_k(G;L;\gamma ;\delta)$      320
Space $\mathfrak{D}$, of complex forms      320
Space $\mathfrak{D}^{pq}$      21
Space $\mathfrak{H^{pq}}$      321
Space $\mathfrak{H}$ of complex harmonic fields $(\delta \varphi = \vartheta \varphi = 0)$      321
Space $\mathfrak{H}^s$      343
Space $\mathfrak{L}^{pq}$, L      319
Space $\mathfrak{L}_p$      288
Spherical harmonics      73 474
Stokes' theorem      290
Strong relative minimum      12
Strongly elliptic system      252
Strongly Lipschitz domain      72
Strongly pseudo-convex boundary      318
Supplementary conditions      211
Tangential coordinate system      321
Tangential part (of a form)      301 302
Topological type (of a Frechet variety)      351
Transversality conditions      2
Uniformly elliptic system      211
Weak convergence in $H_p^m(G)$      70
Weak convergence of maps in $H_p^1$      385
Weak solutions      33
Weakly differentiable functions      97
Weierstrass condition      2 12
Weierstrass E-function      12
Weyl’s lemma      41 42
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