Linear and Quasilinear Parabolic Systems: Sobolev Space Theory - 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 Linear and Quasilinear Parabolic Systems: Sobolev Space Theory write by David Hoff. This book was released on 2020-11-18. Linear and Quasilinear Parabolic Systems: Sobolev Space Theory available in PDF, EPUB and Kindle. This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
Linear and Quasilinear Parabolic Problems
Linear and Quasilinear Parabolic 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 Linear and Quasilinear Parabolic Problems write by Herbert Amann. This book was released on 2012-12-06. Linear and Quasilinear Parabolic Problems available in PDF, EPUB and Kindle. In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.
Qualitative analysis for some quasilinear parabolic systems
Qualitative analysis for some quasilinear parabolic systems - 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 Qualitative analysis for some quasilinear parabolic systems write by Piero de Mottoni. This book was released on 1979. Qualitative analysis for some quasilinear parabolic systems available in PDF, EPUB and Kindle.
Maximal Function Methods for Sobolev Spaces
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.
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Functional Analysis, Sobolev Spaces and Partial Differential Equations - 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 Functional Analysis, Sobolev Spaces and Partial Differential Equations write by Haim Brezis. This book was released on 2010-11-10. Functional Analysis, Sobolev Spaces and Partial Differential Equations available in PDF, EPUB and Kindle. 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.
