On First and Second Order Planar Elliptic Equations with Degeneracies, Abdelhamid Meziani
Автор: Lopez Gomez Julian Название: Linear Second Order Elliptic Operators ISBN: 9814440248 ISBN-13(EAN): 9789814440240 Издательство: World Scientific Publishing Цена: 48570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions.Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators.Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein-Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.
Автор: Qing Han Название: Nonlinear Elliptic Equations of the Second Order ISBN: 1470426072 ISBN-13(EAN): 9781470426071 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 112860.00 T Наличие на складе: Невозможна поставка. Описание: Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kahler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampere equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and ``elementary'' proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.
Автор: Alex Amenta, Pascal Auscher Название: Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach ISBN: 1470442507 ISBN-13(EAN): 9781470442507 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 108680.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy-Sobolev and Besov spaces. The authors use the so-called ``first order approach'' which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations.This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.
Автор: Ariel Barton, Svitlana Mayboroda Название: Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces ISBN: 1470419890 ISBN-13(EAN): 9781470419899 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 83160.00 T Наличие на складе: Невозможна поставка. Описание: Presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable $t$-independent coefficients in spaces of fractional smoothness, in Besov and weighted $L^p$ classes. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.
Автор: Bj?rn Gustafsson; Mihai Putinar Название: Hyponormal Quantization of Planar Domains ISBN: 3319658093 ISBN-13(EAN): 9783319658094 Издательство: Springer Рейтинг: Цена: 32600.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established.
The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.
Автор: Jean-Pierre Francoise; Robert Roussarie Название: Bifurcations of Planar Vector Fields ISBN: 3540535098 ISBN-13(EAN): 9783540535096 Издательство: Springer Рейтинг: Цена: 32560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: A collection of papers on differential equations and dynamical systems which stresses topics relating to Hilbert`s 16th problem. Among these are a solution to Dulac`s problem, results on the multiplicity of singular cycles and results on the zeroes of abelian integrals.
Автор: Yirong Liu, Jibin Li, Wentao Huang Название: Planar Dynamical Systems: Selected Classical Problems ISBN: 3110298295 ISBN-13(EAN): 9783110298291 Издательство: Walter de Gruyter Рейтинг: Цена: 161100.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincare for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago.Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincare and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Автор: Freddy Dumortier; Robert Roussarie; Jorge Sotomayo Название: Bifurcations of Planar Vector Fields ISBN: 3540545212 ISBN-13(EAN): 9783540545217 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This is a treatise on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail, and special analytical tools using abelian integrals are developed.
Автор: John Reyn Название: Phase Portraits of Planar Quadratic Systems ISBN: 1441940243 ISBN-13(EAN): 9781441940247 Издательство: Springer Рейтинг: Цена: 213360.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book attempts to give a presentation of the advance of our knowledge of phase portraits of quadratic systems, paying special attention to the historical development of the subject. This the only book that organizes the portraits into classes, using the notions of finite and infinite multiplicity and finite and infinite index.
Автор: Agmon Shmuel Название: Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29) ISBN: 0691613672 ISBN-13(EAN): 9780691613673 Издательство: Wiley Рейтинг: Цена: 31680.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper
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