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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
Integrand, normal of a parametric problem349 Integrand, of type I96 Integrand, of type II97 Jacobi condition15 Jacobi's equation13 Jensen's inequality21 Kodaira decomposition286298312322 Laplace's equation43 Lebesgue area of a Frechet surface352 Legendre condition210 Legendre — Hadamard condition11 Linear functionals on 70 Linear sets 312 Lipschitz condition4 Lipschitz convergence113 Lipschitz domain (of class )25 Localized inner product301 Localized inner product of complex forms319 Manifold with boundary (of class , etc.)300 Mapping, 453 Mapping, 454 Mapping, 454 Mapping, abcolutely continious379382 Mapping, light489 Mapping, monotone489 Mapping, of class 382 Mapping, of class 379 Maximum principle4061 Mean value properties of harmonic functions4041 Measurable mappings378 Minimizing sequences16 Minimum conditions (on a general elliptic system)215 Minus potential (of a form)310 Multinomial coefficient 63 n-th gradient 4 Norm 338 Norm 337 Norm for complex forms342 Normal coordinate system402 Normal coordinate system centered at a point q on 402 Normal part (of a form)301302 Operator , for complex forms320 Operator , for complex forms319 Operator b, for complex forms319 Operator L, for complex forms321 Operator N, for complex forms321 Order 0[z, ]356357359480 Oriented Frechet variety353 Orthogonal basis332 Parallel geodesic planes443 Parametric representation351 Plus potential (of a form)310 Poincare’s inequality69 Point set distance D(, )406 Poisson’s equation47 Poisson’s integral formula4546 Polyhedral cone460 Potential47 Potential of a form259314 Principal part (of a differential operator)210 Problem of Plateau in 375376 Projection 485 Projection on a geodesic p-plane435 Properly elliptic system211 Quasi-linear equations8 Quasi-potential86 Reflection principle54 Regular mapping64 Regular parametric problem32 Regular Variational problem811 Reifenberg cone inequality459460 Reifenberg's (, R1) condition433 Rellich's theorem75 Riemannian manifold of class 288 Root condition211 Second variation10 Set (S,)406 Sets , 453 Simplicial cone460 Singular integrals50 Slope functions14 Sobolev lemmas7880 Sobolev spaces1920 Sobolev’s embedding theorem80 Space 20288 Space 68 Space (of mappings)378 Space 318 Space 319 Space and 378 Space 320 Space , of complex forms320 Space 21 Space 321 Space of complex harmonic fields 321 Space 343 Space , L319 Space 288 Spherical harmonics73474 Stokes' theorem290 Strong relative minimum12 Strongly elliptic system252 Strongly Lipschitz domain72 Strongly pseudo-convex boundary318 Supplementary conditions211 Tangential coordinate system321 Tangential part (of a form)301302 Topological type (of a Frechet variety)351 Transversality conditions2 Uniformly elliptic system211 Weak convergence in 70 Weak convergence of maps in 385 Weak solutions33 Weakly differentiable functions97 Weierstrass condition212 Weierstrass E-function12 Weyl’s lemma4142