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A First Course in Sobolev Spaces
This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such...
Sobolev Spaces
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
Functional Analysis, Sobolev Spaces and Partial Differential Equations
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Growth of Crystals
Papers from the Sixth All-Union Conference on Growth of Crystals comprise Volume 16 of this series. The articles were chosen with a view to more fully elucidate the basic problems of crystal growth as reflected in domestic and foreign reviews and in original studies. This volume consists of six parts. Part I is devoted to mechanisms of crystal growth that are important for production of materials with given properties. This part examines the temporal evolution of an inhomogeneous state and the array of semicellular and eutectic structures during microstructure formation, the effect of impurity on the nonequi librium vacancy concentration in a growing crystal, and the role of soluble and insoluble impurities in the birth and growth of crystals. Part II deals with the synthesis and electrophysical properties of novel solid electrolytes that are promis ing for practical use, analysis and correlation of the large amount of data on growth by the Bridgman-Stockbar ger method of single crystals of fluorite phases far from stoichiometry, and the hydrothermal chemistry and growth of hexagonal germanium dioxide.
Modern Methods in the Calculus of Variations
This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, w...
Maximal Function Methods for Sobolev Spaces
This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Lebesgue and Sobolev Spaces with Variable Exponents
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.
Growth of Crystals
This 18th volume of the series includes invited papers from the Seventh All-Union Conference on the Growth of Crystals and the Symposium on Molecular-Beam Epitaxy that were held in Moscow in November, 1988. In choosing papers, the Program Committee of the conference gave priority to studies in rapidly emerging areas of the growth and preparation of crystalS and crystalline films. The qualifications of the authors were also consid ered. This ensured that the material was of a high standard and that the problems discussed covered a wide range. These are the same criteria that, we hope, are typical of the volumes of this series. The articles of the present volume are divided into four sections:...
An Introduction to Sobolev Spaces and Interpolation Spaces
After publishing an introduction to the Navier–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.
Functionalized Inorganic Fluorides
Functionalized Inorganic Fluorides: Synthesis, Characterization & Properties of Nanostructured Solids covers several classes of nanostructured and functionalized inorganic fluorides, oxide-fluorides, and fluorinated oxides such as silica and alumina. Ranging from powders or glass-ceramics to thin layers and coatings, they have applications as more efficient and less aggressive catalysts, UV absorbers, planar optical waveguides, integrated lasers and optical amplifiers, luminescent materials, anti-reflective coatings and high Tc superconductors. With a focus on new types of solids, such as nanopowders, hybrids, mesoporous fluorides, and intercalation compounds, the book covers new synthesis routes; physical-chemical characterizations - including morphology, structure, spectroscopic and optical behaviour; detailed ab initio investigations and simulations; and -last but not least- potential applications.
