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This book, first published in 2001, focuses on Poincaré, 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 Poincaré 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 Poincaré'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.

Inequalities (Mathematics) --- Sobolev spaces. --- Spaces, Sobolev --- Function spaces --- Processes, Infinite

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Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.

Sobolev spaces. --- Interpolation spaces. --- Differential equations, Partial. --- Partial differential equations --- Spaces, Interpolation --- Function spaces --- Spaces, Sobolev

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This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.

Ideal spaces. --- Sobolev spaces. --- Function spaces. --- Spaces, Function --- Functional analysis --- Spaces, Sobolev --- Function spaces --- Banach function spaces --- Köthe spaces --- Normed Köthe spaces

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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 acc

Sobolev spaces. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus --- Spaces, Sobolev --- Function spaces --- Analyse fonctionnelle --- Functional analysis --- Sobolev, Espaces de. --- Sobolev, Espaces de --- ELSEVIER-B EPUB-LIV-FT --- Functional analysis. --- Espaces de sobolev

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Analytical spaces --- Analyse fonctionnelle --- Functional analysis --- Sobolev spaces --- Sobolev, Espaces de --- Sobolev spaces. --- #TCPW W8.0 --- 517.982 --- Functional analysis. --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures --- Spaces, Sobolev --- Function spaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Mathematical Theory --- Espaces de sobolev