Friedrich Sauvigny's Books

Partial Differential Equations 1

Foundations and Integral Representations

By: Friedrich Sauvigny

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Partial Differential Equations 1

Foundations and Integral Representations

By: Friedrich Sauvigny

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.

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459

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Springer Science & Business Media

Published Date

ISBN 10

1447129814

ISBN 13

9781447129813

Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

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Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in three-dimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently, as surfaces of zero mean curvature. The final definition of a minimal surface is that of a nonconstant harmonic mapping X: \Omega\to\R^3 which is conformally parametrized on \Omega\subset\R^2 and may have branch points. Thereafter the classical theory of minimal surfaces is surveyed, comprising many examples, a treatment of Björling ́s initial value problem, reflection principles, a formula of the second variation of area, the theorems of Bernstein, Heinz, Osserman, and Fujimoto. The second part of this volume begins with a survey of Plateau ́s problem and of some of its modifications. One of the main features is a new, completely elementary proof of the fact that area A and Dirichlet integral D have the same infimum in the class C(G) of admissible surfaces spanning a prescribed contour G. This leads to a new, simplified solution of the simultaneous problem of minimizing A and D in C(G), as well as to new proofs of the mapping theorems of Riemann and Korn-Lichtenstein, and to a new solution of the simultaneous Douglas problem for A and D where G consists of several closed components. Then basic facts of stable minimal surfaces are derived; this is done in the context of stable H-surfaces (i.e. of stable surfaces of prescribed mean curvature H), especially of cmc-surfaces (H = const), and leads to curvature estimates for stable, immersed cmc-surfaces and to Nitsche ́s uniqueness theorem and Tomi ́s finiteness result. In addition, a theory of unstable solutions of Plateau ́s problems is developed which is based on Courant ́s mountain pass lemma. Furthermore, Dirichlet ́s problem for nonparametric H-surfaces is solved, using the solution of Plateau ́s problem for H-surfaces and the pertinent estimates.

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699

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Springer Science & Business Media

Published Date

ISBN 10

3642116981

ISBN 13

9783642116988

Partial Differential Equations 2

Functional Analytic Methods

By: Friedrich Sauvigny

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Partial Differential Equations 2

Functional Analytic Methods

By: Friedrich Sauvigny

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.

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401

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Springer Science & Business Media

Published Date

ISBN 10

3540344624

ISBN 13

9783540344629

The Communist Manifesto

By: Karl Marx,Friedrich Engels

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The Communist Manifesto

By: Karl Marx,Friedrich Engels

A rousing call to arms whose influence is still felt today Originally published on the eve of the 1848 European revolutions, The Communist Manifesto is a condensed and incisive account of the worldview Marx and Engels developed during their hectic intellectual and political collaboration. Formulating the principles of dialectical materialism, they believed that labor creates wealth, hence capitalism is exploitive and antithetical to freedom. This new edition includes an extensive introduction by Gareth Stedman Jones, Britain's leading expert on Marx and Marxism, providing a complete course for students of The Communist Manifesto, and demonstrating not only the historical importance of the text, but also its place in the world today. For more than seventy years, Penguin has been the leading publisher of classic literature in the English-speaking world. With more than 1,700 titles, Penguin Classics represents a global bookshelf of the best works throughout history and across genres and disciplines. Readers trust the series to provide authoritative texts enhanced by introductions and notes by distinguished scholars and contemporary authors, as well as up-to-date translations by award-winning translators.

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308

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Penguin

Published Date

ISBN 10

0140447571

ISBN 13

9780140447576

Partial Differential Equations 2

Functional Analytic Methods

By: Friedrich Sauvigny

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Partial Differential Equations 2

Functional Analytic Methods

By: Friedrich Sauvigny

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401

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Springer Science & Business Media

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ISBN 10

3540344624

ISBN 13

9783540344629

Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

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Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

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699

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3642116981

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9783642116988

Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny,Anthony Tromba

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Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny,Anthony Tromba

The three-volume treatise consists of the volumes Minimal Surfaces (GL 339), Regularity of Minimal Surfaces (GL 340), and Glolbal Theory of Minimal Surfaces (GL 341) that replace the monograph Minimal Surfaces I , II, published as volumes 295 and 296 of the Grundlehren der mathematischen Wissenschaft series. Ther first volume covers the classical theory as well as existence results concerning boundary value problems for minimal surfaces, in particular results for Plateau's problem. The second volume deals with basic regularity results for minimal surfaces concerning their boundary behaviour at Plateau boundaries and free boundaries. Moreover, exclosure theorems, isoperimetricc inequalities and existence theorems for surfaces of prescribed mean curvature in a Riemanian manifold and for the thread problem are discussed. Finally, the third volume deals with geometric properties of minimal surfaces with free boundaries and with a priori gradient estimates for n-dimensional minimal surfaces, leading to various Bernstein-type theorems. Secondly, a global theory of minimal surfaces (as envisioned by Smale) is presented, including index theorems.

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1910

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Springer

Published Date

ISBN 10

3642117155

ISBN 13

9783642117152

Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

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Minimal Surfaces

By: Ulrich Dierkes,Stefan Hildebrandt,Friedrich Sauvigny

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692

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Springer

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ISBN 10

3642265278

ISBN 13

9783642265273

Book's by Friedrich Sauvigny

Partial Differential Equations 1

Partial Differential Equations 1

Minimal Surfaces

Minimal Surfaces

Partial Differential Equations 2

Partial Differential Equations 2

The Communist Manifesto

The Communist Manifesto

Partial Differential Equations 2

Partial Differential Equations 2

Minimal Surfaces

Minimal Surfaces

Minimal Surfaces

Minimal Surfaces

Minimal Surfaces

Minimal Surfaces

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