Young Measures and Compactness in Measure Spaces, Liviu C. Florescu, Christiane Godet-Thobie

Автор: M. Ursul
Название: Topological Rings Satisfying Compactness Conditions
ISBN: 9401039461 ISBN-13(EAN): 9789401039468
Издательство: Springer
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Автор: Liviu C. Florescu, Christiane Godet-Thobie
Название: Young Measures and Compactness in Measure Spaces
ISBN: 3110276402 ISBN-13(EAN): 9783110276404
Издательство: Walter de Gruyter
Цена: 185890.00 T
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Описание: In recent years, technological progress created a great need for complex mathematical models. Many practical problems can be formulated using optimization theory and they hope to obtain an optimal solution. In most cases, such optimal solution can not be found. So, non-convex optimization problems (arising, e.g., in variational calculus, optimal control, nonlinear evolutions equations) may not possess a classical minimizer because the minimizing sequences have typically rapid oscillations. This behavior requires a relaxation of notion of solution for such problems; often we can obtain such a relaxation by means of Young measures. This monograph is a self-contained book which gathers all theoretical aspects related to the defining of Young measures (measurability, disintegration, stable convergence, compactness), a book which is also a useful tool for those interested in theoretical foundations of the measure theory. It provides a complete set of classical and recent compactness results in measure and function spaces.The book is organized in three chapters: The first chapter covers background material on measure theory in abstract frame. In the second chapter the measure theory on topological spaces is presented. Compactness results from the first two chapters are used to study Young measures in the third chapter. All results are accompanied by full demonstrations and for many of these results different proofs are given. All statements are fully justified and proved.

Автор: D. K. Haley
Название: Equational Compactness in Rings
ISBN: 3540095489 ISBN-13(EAN): 9783540095484
Издательство: Springer
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Автор: C. Dafermos; J.L. Ericksen; D. Kinderlehrer; M. Sl
Название: Oscillation Theory, Computation, and Methods of Compensated Compactness
ISBN: 1461386918 ISBN-13(EAN): 9781461386919
Издательство: Springer
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Цена: 113190.00 T
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Описание: This IMA Volume in Mathematics and its Applications Oscillation Theory, Computation, and Methods of Compensated Compactness represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS. We are grateful to the Scientific Committee: J. L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger PREFACE Historically, one of the most important prohlems in continuum mechanics has been the treatment of nonlinear hyperbolic systems of conservation laws. Thp. importance of these systems lies in the fact that the underlyinq equ tions of mass, momentum, and energy are descrihed by conservation laws. Their nonlinearity and hyperbolicity are consequences of some cornmon constitutive relations, for example, in an ideal gas. The I. M. A. Workshop on "Osci 11 at i on theory. computat i on, and methods of com- pensated compactness" brought together scientists from both the analytical and numerical sides of conservation law research. The goal was to examine recent trends in the investigation of systems of conservation laws and in particular to focus on the roles of dispersive and diffusive limits for singularily perturbed conservation laws. Special attention was devoted to the new ideas of compen- sated compactness and oscillation theory.

Автор: Christoph Hummel
Название: Gromov`s Compactness Theorem for Pseudo-holomorphic Curves
ISBN: 3034898428 ISBN-13(EAN): 9783034898423
Издательство: Springer
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Описание: This book presents the original proof of Gromov`s compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint.

Автор: Charles Castaing; Paul Raynaud de Fitte; Michel Va
Название: Young Measures on Topological Spaces
ISBN: 1402019637 ISBN-13(EAN): 9781402019630
Издательство: Springer
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Описание: Aims to provides applications to Visintin and Reshetnyak type theorems (Chapters 6 and 8), existence of solutions to differential inclusions (Chapter 7), dynamical programming (Chapter 8) and the Central Limit Theorem in locally convex spaces (Chapter 9).

Автор: Charles Castaing; Paul Raynaud de Fitte; Michel Va
Название: Young Measures on Topological Spaces
ISBN: 9048165520 ISBN-13(EAN): 9789048165520
Издательство: Springer
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Описание: Classicalexamples of moreand more oscillatingreal-valued functions on a domain N ?of R are the functions u (x)=sin(nx)with x=(x, ..., x ) or the so-called n 1 1 n n+1 Rademacherfunctionson]0,1 , u (x)=r (x) = sgn(sin(2 x))(seelater3.1.4). n n They may appear as the gradients?v of minimizing sequences (v ) in some n n n?N variationalproblems. Intheseexamples, thefunctionu convergesinsomesenseto n ameasure on ? R, called Young measure. In Functional Analysis formulation, this is the narrow convergence to of the image of the Lebesgue measure on ? by ? ? (?, u (?)). In the disintegrated form ( ), the parametrized measure n ? ? captures the possible scattering of the u around ?. n Curiously if (X ) is a sequence of random variables deriving from indep- n n?N dent ones, the n-th one may appear more and more far from the k ?rst ones as 2 if it was oscillating (think of orthonormal vectors in L which converge weakly to 0). More precisely when the laws L(X ) narrowly converge to some probability n measure, it often happens that for any k and any A in the algebra generated by X, ..., X, the conditional law L(XA) still converges to (see Chapter 9) 1 k n which means 1 C (R) ?(X (?))dP(?) d b n P(A) A R or equivalently, ? denoting the image of P by ? ? (?, X (?)), n X n (1l )d? (1l )d P? ].