Описание: This self-contained book is excellent for graduate-level courses devoted to variational analysis, optimization, and partial differential equations (PDEs). It provides readers with a complete guide to problems in these fields as well as a detailed presentation of the most important tools and methods of variational analysis. New trends in variational analysis are also presented, along with recent developments and applications in this area. It contains several applications to problems in geometry, mechanics, elasticity, and computer vision, along with a complete list of references. The book is divided into two parts. In Part I, classical Sobolev spaces are introduced and the reader is provided with the basic tools and methods of variational analysis and optimization in infinite dimensional spaces, with applications to classical PDE problems. In Part II, BV spaces are introduced and new trends in variational analysis are presented.
Описание: This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision.Among the new elements in this second edition: the section of Chapter 5 on capacity theory and elements of potential theory now includes the concepts of quasi-open sets and quasi-continuity; Chapter 6 includes an increased number of examples in the areas of linearized elasticity system, obstacles problems, convection-diffusion, and semilinear equations; Chapter 11 has been expanded to include a section on mass transportation problems and the Kantorovich relaxed formulation of the Monge problem; a new subsection on stochastic homogenization in Chapter 12 establishes the mathematical tools coming from ergodic theory, and illustrates them in the scope of statistically homogeneous materials; Chapter 16 has been augmented by examples illustrating the shape optimization procedure; and Chapter 17 is an entirely new and comprehensive chapter devoted to gradient flows and the dynamical approach to equilibria.
Описание: S.L. Sobolev (1908вЂ“1989) was a great mathematician of the twentieth century. His selected works included in this volume laid the foundations for intensive development of the modern theory of partial differential equations and equations of mathematical physics, and they were a gold mine for new directions of functional analysis and computational mathematics.The topics covered in this volume include SobolevвЂ™s fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access.
Описание: After publishing an introduction to the NavierвЂ“Stokes equation and oceanography (Vol. 1 of this series), Luc Tartar follows with another set of lecture notes based on a graduate course in two parts, as indicated by the title. A draft has been available on the internet for a few years. The author has now revised and polished it into a text accessible to a larger audience.
Автор: Robert A. Adams Название: Sobolev Spaces,140 ISBN: 0120441438 ISBN-13(EAN): 9780120441433 Издательство: Elsevier Science Цена: 13464 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.
This second edition of Adam's 'classic' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.
Self-contained and accessible for readers in other disciplines
Written at elementary level making it accessible to graduate students
Автор: Hebey Название: Sobolev Spaces on Riemannian Manifolds ISBN: 3540617221 ISBN-13(EAN): 9783540617228 Издательство: Springer Рейтинг: Цена: 2520 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work discusses developments in the theory of Sobolev spaces on Riemannian manifolds. Hebey`s presentation includes developments due mainly to the author himself and to Hebey Vaugon, and he discusses the hypotheses to test whether they can be weakened.
Описание: The book systematically develops nonlinear potential theory and the Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincare inequalities, Maz`ya type embedding theorems, and isoperimetric inequalities.
Автор: Maz`ya Название: Sobolev Spaces ISBN: 3642155634 ISBN-13(EAN): 9783642155635 Издательство: Springer Рейтинг: Цена: 14024 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume ?rst appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a signi?cantly augmented list of references aim to create a broader and modern view of the area.
Описание: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
Автор: Heinonen Название: Sobolev Spaces on Metric Measure Spaces ISBN: 1107092345 ISBN-13(EAN): 9781107092341 Издательство: Cambridge Academ Рейтинг: Цена: 9574 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincare inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincare inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincare inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincare inequalities.
Автор: Laurent Saloff-Coste Название: Aspects of Sobolev-Type Inequalities ISBN: 0521006074 ISBN-13(EAN): 9780521006071 Издательство: Cambridge Academ Рейтинг: Цена: 7389 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on Poincare, Nash and other Sobolev-type inequalities and their applications to the Laplace and heat diffusion equations on Riemannian manifolds. Applications covered include the ultracontractivity of the heat diffusion semigroup, Gaussian heat kernel bounds, the Rozenblum-Lieb-Cwikel inequality and elliptic and parabolic Harnack inequalities. Emphasis is placed on the role of families of local Poincare and Sobolev inequalities. The text provides the first self contained account of the equivalence between the uniform parabolic Harnack inequality, on the one hand, and the conjunction of the doubling volume property and Poincare’s inequality on the other. It is suitable to be used as an advanced graduate textbook and will also be a useful source of information for graduate students and researchers in analysis on manifolds, geometric differential equations, Brownian motion and diffusion on manifolds, as well as other related areas.
Автор: Maz`ya, Vladimir G. Shaposhnikova, T.o. Название: Theory of sobolev multipliers ISBN: 3540694900 ISBN-13(EAN): 9783540694908 Издательство: Springer Рейтинг: Цена: 15427 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers a comprehensive exposition of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. This book covers topics such as: trace inequalities, analytic characterization of multipliers, relations between spaces of Sobolev multipliers and other function spaces, and maximal subalgebras of multiplier spaces.
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