Author: Wolfgang Tutschke
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 300

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Book Description

Author: Joseph Wloka
Publisher: Cambridge University Press
ISBN: 9780521277594
Category : Mathematics
Languages : en
Pages : 536

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Book Description
A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.

Author: C. Carath‚odory
Publisher: American Mathematical Society
ISBN: 1470478978
Category : Mathematics
Languages : en
Pages : 418

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Book Description
From the Preface: The book consists of two parts. In the first part, I have made an attempt to simplify the presentation of the theory of partial differential equations to the first order so that its study will require little time and also be accessible to the average student of mathematics ? The second part, which contains the Calculus of Variations, can also be read independently if one refers back to earlier sections in Part I ? I have never lost sight of the fact that the Calculus of Variations, as it is presented in Part II, should above all be a servant of Mechanics. Therefore, I have in particular prepared everything from the very outset for treatment in multidimensional spaces. In this second English edition of Carath‚odory's famous work, the two volumes of the first edition have been combined into one (with a combination of the two indexes into a single index). There is a deep and fundamental relationship between the differential equations that occur in the calculus of variations and partial differential equations of the first order: in particular, to each such partial differential equation there correspond variational problems. This basic fact forms the rationale for Carath‚odory's masterpiece.

Author: Friedrich Sauvigny
Publisher: Springer Science & Business Media
ISBN: 3540344594
Category : Mathematics
Languages : en
Pages : 453

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Book Description
This comprehensive two-volume textbook covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is placed on the connection of PDEs and complex variable methods. In this first volume the following topics are treated: Integration and differentiation on manifolds, Functional analytic foundations, Brouwer's degree of mapping, Generalized analytic functions, Potential theory and spherical harmonics, Linear partial differential equations. We solve partial differential equations via integral representations in this volume, reserving functional analytic solution methods for Volume Two.

Author: Friedrich Sauvigny
Publisher: Springer Science & Business Media
ISBN: 1447129814
Category : Mathematics
Languages : en
Pages : 459

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Book Description
This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated: • integration and differentiation on manifolds • foundations of functional analysis • Brouwer's mapping degree • generalized analytic functions • potential theory and spherical harmonics • linear partial differential equations This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. The second volume will present functional analytic methods and applications to problems in differential geometry. This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.

Author: Lipman Bers
Publisher: American Mathematical Soc.
ISBN: 0821800493
Category : Mathematics
Languages : en
Pages : 370

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Book Description
Divided in two main parts, this title contains an assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. Suitable for graduate students and researchers interested in partial differential equations, it also includes a discussion of some quasi-linear elliptic equations.

Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 0387215956
Category : Mathematics
Languages : en
Pages : 331

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Book Description
Modern and systematic treatment of main approaches; Several additions have been made to the German edition, most notably coverage of eigenvalues and expansions; Emphasis on methods relevant for both linear and nonlinear equations; Contains chapter summaries, detailed illustrations and numerous exercises

Author: Dorothy L. Bernstein
Publisher: Princeton University Press
ISBN: 1400882222
Category : Mathematics
Languages : en
Pages : 228

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Book Description
The description for this book, Existence Theorems in Partial Differential Equations. (AM-23), Volume 23, will be forthcoming.

Author: Friedrich Sauvigny
Publisher: Springer Science & Business Media
ISBN: 3540344624
Category : Mathematics
Languages : en
Pages : 401

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Book Description
This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.

Author: Michael Demuth
Publisher: Birkhäuser
ISBN: 3034890923
Category : Mathematics
Languages : en
Pages : 422

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Book Description
The book contains the contributions to the conference on "Partial Differential Equations" held in Holzhau (Germany) in July 1994, where outstanding specialists from analysis, geometry and mathematical physics reviewed recent progress and new interactions in these areas. Topics of special interest at the conference and which now form the core of this volume are hyperbolic operators, spectral theory for elliptic operators, eta-invariant, singular configura- tions and asymptotics, Bergman-kernel, attractors of non-autonomous evolution equations, pseudo-differential boundary value problems, Mellin pseudo- differential operators, approximation and stability problems for elliptic operators, and operator determinants. In spectral theory adiabatic and semiclassical limits, Dirichlet decoupling and domain perturbations, capacity of obstacles, limiting absorption problems, N-body scattering, and number of bound states are considered. Schrödinger operators are studied with magnetic fields, with random and with many-body potentials, and for nonlinear problems. In semigroup theory the Feller property, errors for product formulas, fractional powers of generators, and functional integration for relativistic semigroups are analyzed.