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Author: Nikolaĭ Nikolaevich Tarkhanov
Publisher: De Gruyter Akademie Forschung
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
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.
Author: Nikolaĭ Nikolaevich Tarkhanov
Publisher: De Gruyter Akademie Forschung
ISBN:
Category : Mathematics
Languages : en
Pages : 488
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Book Description
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.
Author: C.V. Pao
Publisher: Springer Science & Business Media
ISBN: 1461530342
Category : Mathematics
Languages : en
Pages : 786
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Book Description
In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.
Author: E. M. Landis
Publisher: American Mathematical Soc.
ISBN: 9780821897812
Category : Mathematics
Languages : en
Pages : 224
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Book Description
Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity. The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Author: Carlos E. Kenig
Publisher: American Mathematical Soc.
ISBN: 0821803093
Category : Mathematics
Languages : en
Pages : 162
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Book Description
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.
Author: Antonino Maugeri
Publisher: Wiley-VCH
ISBN:
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This book unifies the different approaches in studying elliptic and parabolic partial differential equations with discontinuous coefficients. To the enlarging market of researchers in applied sciences, mathematics and physics, it gives concrete answers to questions suggested by non-linear models. Providing an up-to date survey on the results concerning elliptic and parabolic operators on a high level, the authors serve the reader in doing further research. Being themselves active researchers in the field, the authors describe both on the level of good examples and precise analysis, the crucial role played by such requirements on the coefficients as the Cordes condition, Campanato's nearness condition, and vanishing mean oscillation condition. They present the newest results on the basic boundary value problems for operators with VMO coefficients and non-linear operators with discontinuous coefficients and state a lot of open problems in the field.
Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486469190
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Largely self-contained, this three-part treatment focuses on elliptic and evolution equations, concluding with a series of independent topics directly related to the methods and results of the preceding sections. 1969 edition.
Author: Kari Astala
Publisher: Princeton University Press
ISBN: 1400830117
Category : Mathematics
Languages : en
Pages : 696
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Book Description
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.
Author: George Norman Trytten
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 92
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Book Description
An analysis is presented which deals with a technique for approximating the solution to a Cauchy problem for a geneal second-order elliptic patil differential equation defined in an N-dimensional region D. The method is based upon the determination of an a priori bound for the value of an arbitrary function u at a point P in D in terms of the values of u and its gradient on the cauchy surface andA FUNCTIONAL OF THE ELLIPTIC OPERATOR APPLIED TO U. (Author).
Author: Mourad Choulli
Publisher: Springer
ISBN: 3319336428
Category : Mathematics
Languages : en
Pages : 88
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Book Description
This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.
Author: Victor Isakov
Publisher: Springer Science & Business Media
ISBN: 1489900306
Category : Mathematics
Languages : en
Pages : 296
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Book Description
A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.
