Maximal Function Methods for Sobolev Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximal Function Methods for Sobolev Spaces write by Juha Kinnunen. This book was released on 2021-08-02. Maximal Function Methods for Sobolev Spaces available in PDF, EPUB and Kindle. 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.
Theory of Function Spaces II
Theory of Function Spaces II - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Theory of Function Spaces II write by Hans Triebel. This book was released on 2010-05-18. Theory of Function Spaces II available in PDF, EPUB and Kindle.
Fractional Sobolev Spaces and Inequalities
Fractional Sobolev Spaces and Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fractional Sobolev Spaces and Inequalities write by D. E. Edmunds. This book was released on 2022-10-13. Fractional Sobolev Spaces and Inequalities available in PDF, EPUB and Kindle. The fractional Sobolev spaces studied in the book were introduced in the 1950s by Aronszajn, Gagliardo and Slobodeckij in an attempt to fill the gaps between the classical Sobolev spaces. They provide a natural home for solutions of a vast, and rapidly growing, number of questions involving differential equations and non-local effects, ranging from financial modelling to ultra-relativistic quantum mechanics, emphasising the need to be familiar with their fundamental properties and associated techniques. Following an account of the most basic properties of the fractional spaces, two celebrated inequalities, those of Hardy and Rellich, are discussed, first in classical format (for which a survey of the very extensive known results is given), and then in fractional versions. This book will be an Ideal resource for researchers and graduate students working on differential operators and boundary value problems.
New Analytic and Geometric Methods in Inverse Problems
New Analytic and Geometric Methods in Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Analytic and Geometric Methods in Inverse Problems write by Kenrick Bingham. This book was released on 2013-04-17. New Analytic and Geometric Methods in Inverse Problems available in PDF, EPUB and Kindle. In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.
Maximal Cohen–Macaulay Modules and Tate Cohomology
Maximal Cohen–Macaulay Modules and Tate Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Maximal Cohen–Macaulay Modules and Tate Cohomology write by Ragnar-Olaf Buchweitz. This book was released on 2021-12-16. Maximal Cohen–Macaulay Modules and Tate Cohomology available in PDF, EPUB and Kindle. This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.
