Author: Giovanni Leoni
Publisher: American Mathematical Society
Keywords: studies, mathematics, graduate, spaces, course, sobolev, first
Number of Pages: 607
Published: 2009-07-15
List price: $85.00
ISBN-10: 0821847686
ISBN-13: 9780821847688
Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications
Author: Victor I. Burenkov
Publisher: B. G. Teubner Gmbh
Keywords: veroffentlichungen, rechtswissenschaftliche, domains, spaces, sobolev
Number of Pages: 312
Published: 1998-01
List price: unknow
ISBN-10: 3815420687
ISBN-13: 9783815420683
Author: J.W. Neuberger
Publisher: Springer
Keywords: notes, mathematics, lecture, equations, gradients, differential, sobolev
Number of Pages: 289
Published: 2009-12-01
List price: $59.95
ISBN-10: 3642040403
ISBN-13: 9783642040405
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside f
Author: Emmanuel Hebey
Publisher: Springer
Keywords: notes, mathematics, lecture, manifolds, spaces, riemannian, sobolev
Number of Pages: 116
Published: 1996-10-02
List price: $34.95
ISBN-10: 3540617221
ISBN-13: 9783540617228
Several books deal with Sobolev spaces on open subsets of R (n), but none yet with Sobolev spaces on Riemannian manifolds, despite the fact that the theory of Sobolev spaces on Riemannian manifolds already goes back about 20 years. The book of Emmanuel Hebey will fill this gap, and become a necessary reading for all using Sobolev spaces on Riemannian manifolds. Hebey’s presentation is very detailed, and includes the most recent developments due mainly to the author himself and to Hebey-Vaugon. He makes numerous things more precise, and discusses the hypotheses to test whether they can be
Author: Qi S. Zhang
Publisher: CRC Press
Keywords: flow, poincare, conjecture, ricci, kernels, inequalities, heat, sobolev
Number of Pages: 432
Published: 2010-07-02
List price: $79.95
ISBN-10: 1439834598
ISBN-13: 9781439834596
Focusing on Sobolev inequalities and their applications to analysis on manifolds and Ricci flow, Sobolev Inequalities, Heat Kernels under Ricci Flow, and the Poincaré Conjecture introduces the field of analysis on Riemann manifolds and uses the tools of Sobolev imbedding and heat kernel estimates to study Ricci flows, especially with surgeries. The author explains key ideas, difficult proofs, and important applications in a succinct, accessible, and unified manner. The book first discusses Sobolev inequalities in various settings, including the Euclidean case, the Riemannian case, and the
Author: Haim Brezis
Publisher: Springer
Keywords: differential, equations, universitext, partial, spaces, analysis, sobolev, functional
Number of Pages: 456
Published: 2010-07-20
List price: $59.95
ISBN-10: 0387709134
ISBN-13: 9780387709130
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
Author: Emmanuel Hebey
Publisher: American Mathematical Society
Keywords: courant, lecture, notes, inequalities, spaces, analysis, manifolds, sobolev, nonlinear
Number of Pages: 290
Published: 2000-12-01
List price: $36.00
ISBN-10: 0821827006
ISBN-13: 9780821827000
This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. "Several surprising phenomena appear when studying Sobolev spaces on manifolds," according to the author. "Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role." The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces
