Elliptic Systems in the Plane
Author: Wolfgang L. Wendland
Publisher: Pitman Publishing
Published: 1979
Total Pages: 424
ISBN-13:
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Boundary Value Problems for Elliptic Systems
Author: J. T. Wloka
Publisher: Cambridge University Press
Published: 1995-07-28
Total Pages: 659
ISBN-13: 0521430119
DOWNLOAD EBOOK →The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.
First Order Elliptic Systems: A Function Theoretic Approach
Author: Buchanan
Publisher: Academic Press
Published: 1983-07-19
Total Pages: 280
ISBN-13: 0080956696
DOWNLOAD EBOOK →First Order Elliptic Systems: A Function Theoretic Approach
Boundary-value Problems with Free Boundaries for Elliptic Systems of Equations
Author: Valentin Nikolaevich Monakhov
Publisher: American Mathematical Soc.
Published: 1983
Total Pages: 540
ISBN-13: 9780821898079
DOWNLOAD EBOOK →This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and problems in elastico-plasticity.
Analysis as a Life
Author: Sergei Rogosin
Publisher: Springer
Published: 2019-01-30
Total Pages: 318
ISBN-13: 3030026507
DOWNLOAD EBOOK →This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday. It aims at being a tribute to the excellent achievements of Heinrich Begehr in complex analysis and complex differential equations, and especially to his prominent role as one of the creators and long-time leader of the International Society for Analysis, its Applications and Computation (ISAAC).
Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)
Author: Kari Astala
Publisher: Princeton University Press
Published: 2009-01-18
Total Pages: 708
ISBN-13: 9780691137773
DOWNLOAD EBOOK →This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Singular Partial Differential Equations
Author: Abduhamid Dzhuraev
Publisher: CRC Press
Published: 1999-11-29
Total Pages: 220
ISBN-13: 9781584881445
DOWNLOAD EBOOK →Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain. Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others. Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians.
Partial Differential Equations of Elliptic Type
Author: C. Miranda
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 384
ISBN-13: 3642877737
DOWNLOAD EBOOK →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.
Elliptic Partial Differential Equations
Author: Vitaly Volpert
Publisher: Springer Science & Business Media
Published: 2011-03-03
Total Pages: 649
ISBN-13: 3034605374
DOWNLOAD EBOOK →The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments . The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.
Degenerate and Other Problems
Author: Abduhamid Dzhuraev
Publisher: CRC Press
Published: 2020-10-07
Total Pages: 328
ISBN-13: 100015808X
DOWNLOAD EBOOK →This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.
