Hardy Inequalities and Applications to the Dirichlet Problem on Fractal Domanins PDF Download
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Author: Kaj Nyström
Publisher:
ISBN:
Category :
Languages : en
Pages : 54
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Book Description
Author: Kaj Nyström
Publisher:
ISBN:
Category :
Languages : en
Pages : 54
Get Book Here
Book Description
Author: Kaj Nyström
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Nikolai Kutev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110980371
Category : Mathematics
Languages : en
Pages : 158
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Book Description
This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.
Author: Vladimir G Maz'ya
Publisher: World Scientific
ISBN: 9814498564
Category : Mathematics
Languages : en
Pages : 502
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Book Description
The spaces of functions with derivatives in Lp, called the Sobolev spaces, play an important role in modern analysis. During the last decades, these spaces have been intensively studied and by now many problems associated with them have been solved. However, the theory of these function classes for domains with nonsmooth boundaries is still in an unsatisfactory state.In this book, which partially fills this gap, certain aspects of the theory of Sobolev spaces for domains with singularities are studied. We mainly focus on the so-called imbedding theorems, extension theorems and trace theorems that have numerous applications to partial differential equations. Some of such applications are given.Much attention is also paid to counter examples showing, in particular, the difference between Sobolev spaces of the first and higher orders. A considerable part of the monograph is devoted to Sobolev classes for parameter dependent domains and domains with cusps, which are the simplest non-Lipschitz domains frequently used in applications.This book will be interesting not only to specialists in analysis but also to postgraduate students.
Author: Michael Ruzhansky
Publisher: Springer
ISBN: 303002895X
Category : Mathematics
Languages : en
Pages : 579
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Book Description
This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Author: Alexander A. Balinsky
Publisher: Springer
ISBN: 3319228706
Category : Mathematics
Languages : en
Pages : 277
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Book Description
This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
Author: Everitt
Publisher: CRC Press
ISBN: 9780824784881
Category : Mathematics
Languages : en
Pages : 306
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Book Description
Proceedings of an international conference organized by the London Mathematical Society, held July 1987 at the U. of Birmingham, and dominated by the ghosts of Hardy, Littlewood and Polya, whose Inequalities (still the primary reference in the field) appeared in 1934. Thirteen essays summarize subse
Author: Anders Vretblad
Publisher:
ISBN:
Category : Congresses
Languages : en
Pages : 276
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Book Description
Author: Dorin Andrica
Publisher: Springer Nature
ISBN: 3030274071
Category : Mathematics
Languages : en
Pages : 848
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Book Description
Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Author: Edward Norman Dancer
Publisher: American Mathematical Soc.
ISBN: 0821825631
Category : Mathematics
Languages : en
Pages : 81
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Book Description
In this paper, we discuss the existence, uniqueness and asymptotic behavior of positive solutions of the equation −[capital Greek]Delta[italic]u = [lowercase Greek]Lambda[function]ƒ([italic]u) in [capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n], [and] [italic]u = 0 on [partial derivative/boundary/degree of a polynomial symbol]([capital Greek]Omega[surmounted by macron] [times symbol] [−[italic]n, [italic]n]) for [italic]n large. Here [capital Greek]Omega[surmounted by macron] is a bounded domain in [italic capital]R[superscript italic]k with smooth boundary. Note that by rescaling the equation (including [lowercase Greek]Lambda), our theory covers problems on domains ([set membership symbol][capital Greek]Omega[surmounted by macron]) [times symbol] [−1,1] where [set membership symbol] is small.
