Nonlinear Analysis on Manifolds: 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 Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities write by Emmanuel Hebey. This book was released on 2000-10-27. Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities available in PDF, EPUB and Kindle. 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 for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
Sobolev Spaces in Mathematics I
Sobolev Spaces in Mathematics I - 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 Sobolev Spaces in Mathematics I write by Vladimir Maz'ya. This book was released on 2008-12-02. Sobolev Spaces in Mathematics I available in PDF, EPUB and Kindle. This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.
Sobolev Spaces in Mathematics II
Sobolev Spaces in Mathematics 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 Sobolev Spaces in Mathematics II write by Vladimir Maz'ya. This book was released on 2008-11-26. Sobolev Spaces in Mathematics II available in PDF, EPUB and Kindle. Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Sobolev Spaces on Riemannian Manifolds
Sobolev Spaces on Riemannian Manifolds - 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 Sobolev Spaces on Riemannian Manifolds write by Emmanuel Hebey. This book was released on 2006-11-14. Sobolev Spaces on Riemannian Manifolds available in PDF, EPUB and Kindle. 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 weakened, and also presents new results.
Function Spaces, Differential Operators and Nonlinear Analysis
Function Spaces, Differential Operators and Nonlinear Analysis - 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 Function Spaces, Differential Operators and Nonlinear Analysis write by Dorothee Haroske. This book was released on 2012-12-06. Function Spaces, Differential Operators and Nonlinear Analysis available in PDF, EPUB and Kindle. This volume is dedicated to our teacher and friend Hans Triebel. The core of the book is based on lectures given at the International Conference "Function Spaces, Differential Operators and Nonlinear Analysis" (FSDONA--01) held in Teistungen, Thuringia / Germany, from June 28 to July 4,2001, in honour of his 65th birthday. This was the fifth in a series of meetings organised under the same name by scientists from Finland (Helsinki, Oulu) , the Czech Republic (Prague, Plzen) and Germany (Jena) promoting the collaboration of specialists in East and West, working in these fields. This conference was a very special event because it celebrated Hans Triebel's extraordinary impact on mathematical analysis. The development of the mod ern theory of function spaces in the last 30 years and its application to various branches in both pure and applied mathematics is deeply influenced by his lasting contributions. In a series of books Hans Triebel has given systematic treatments of the theory of function spaces from different points of view, thus revealing its interdependence with interpolation theory, harmonic analysis, partial differential equations, nonlinear operators, entropy, spectral theory and, most recently, anal ysis on fractals. The presented collection of papers is a tribute to Hans Triebel's distinguished work. The book is subdivided into three parts: • Part I contains the two invited lectures by O.V. Besov (Moscow) and D.E. Edmunds (Sussex) having a survey character and honouring Hans Triebel's contributions.
