Download or read book On Uniqueness in Cauchy Problems for Elliptic Systems of Equations written by Avron Douglis and published by . This book was released on 1960 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uniqueness and Non Uniqueness in the Cauchy Problem written by Zuily and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elliptic Equations An Introductory Course written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2009-02-19 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.
Download or read book Partial Differential Equations of Elliptic Type written by C. Miranda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.
Download or read book First Order Elliptic Systems A Function Theoretic Approach written by Buchanan and published by Academic Press. This book was released on 1983-07-19 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Order Elliptic Systems: A Function Theoretic Approach
Download or read book The Cauchy Problem for Solutions of Elliptic Equations written by Nikolaĭ Nikolaevich Tarkhanov and published by De Gruyter Akademie Forschung. This book was released on 1995 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an attempt to bring together various topics in partial differential equations related to the Cauchy problem for solutions of an elliptic equation. Ever since Hadamard, the Cauchy problem for solutions of elliptic equations has been known to be ill-posed.
Download or read book Some Classes of Partial Differential Equations written by Andreĭ Vasilʹevich Bit︠s︡adze and published by CRC Press. This book was released on 1988 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic examination of classical and non-classical problems for linear partial differential equations and systems of elliptic, hyperbolic and mixed types. Among a number of difficult problems addressed are the Dirichlet and oblique derivative problems for non- uniformly elliptic equations and non-strongly elliptic systems and the Cauchy and Darloux problems for non-strongly hyperbolic systems and hyperbolic equations with parabolic degeneracy on the boundary. Written at a level suitable for undergraduate and graduate students and researchers. Individual price, $89. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Uniqueness Problems for Degenerating Equations and Nonclassical Problems written by S. P. Shishatskii and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Download or read book Partial Differential Equations written by Lipman Bers and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.
Download or read book Unique Continuation for Elliptic Equations written by Murray H. Protter and published by . This book was released on 1959 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Value Problems For Second Order Elliptic Equations written by A.V. Bitsadze and published by Elsevier. This book was released on 2012-12-02 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-chapter text is devoted to a study of the basic linear boundary value problems for linear second order partial differential equations, which satisfy the condition of uniform ellipticity. The opening chapter deals with the fundamental aspects of the linear equations theory in normed linear spaces. This topic is followed by discussions on solutions of elliptic equations and the formulation of Dirichlet problem for a second order elliptic equation. A chapter focuses on the solution equation for the directional derivative problem. Another chapter surveys the formulation of the Poincaré problem for second order elliptic systems in two independent variables. This chapter also examines the theory of one-dimensional singular integral equations that allow the investigation of highly important classes of boundary value problems. The final chapter looks into other classes of multidimensional singular integral equations and related boundary value problems.
Download or read book Selected Works of Lipman Bers written by Lipman Bers and published by American Mathematical Soc.. This book was released on 1998 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Analysis of Solutions of Elliptic Equations written by Nikolai Tarkhanov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.
Download or read book Carleman Estimates and Applications to Uniqueness and Control Theory written by Feruccio Colombini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.
Download or read book Elliptic Systems in the Plane written by Wolfgang L. Wendland and published by Pitman Publishing. This book was released on 1979 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse and Improperly Posed Problems in Differential Equations written by G. Anger and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Constructive Methods for Elliptic Equations written by R.P. Gilbert and published by Springer. This book was released on 2006-11-15 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily these lectures are a report on recent work by the Indiana University group working on Function theoretic methods as applied to the theory of partial differential equations.
