On Boundary Regularity For The Plateau Problem
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On Boundary Regularity For The Plateau Problem
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Author : William Kenneth Allard
language : en
Publisher:
Release Date : 1968
On Boundary Regularity For The Plateau Problem written by William Kenneth Allard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Boundary Regularity For The Plateau Problem
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Author : Simone Steinbrüchel
language : en
Publisher:
Release Date : 2022
Boundary Regularity For The Plateau Problem written by Simone Steinbrüchel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Minimal Surfaces Ii
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Minimal Surfaces Ii written by Ulrich Dierkes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
Minimal Surfaces I is an introduction to the field of minimal surfaces and a presentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can also be useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory for nonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
Regularity Of Minimal Surfaces
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Regularity Of Minimal Surfaces written by Ulrich Dierkes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Mathematics categories.
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general Gauss-Bonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is that, for principal reasons, it is impossible to derive a priori estimates. Therefore regularity proofs for non-minimizers have to be based on indirect reasoning using monotonicity formulas. This is followed by a long chapter discussing geometric properties of minimal and H-surfaces such as enclosure theorems and isoperimetric inequalities, leading to the discussion of obstacle problems and of Plateau ́s problem for H-surfaces in a Riemannian manifold. A natural generalization of the isoperimetric problem is the so-called thread problem, dealing with minimal surfaces whose boundary consists of a fixed arc of given length. Existence and regularity of solutions are discussed. The final chapter on branch points presents a new approach to the theorem that area minimizing solutions of Plateau ́s problem have no interior branch points.
Minimal Surfaces Boundary Regularity
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Author : Ulrich Dierkes
language : en
Publisher: Springer
Release Date : 1992
Minimal Surfaces Boundary Regularity written by Ulrich Dierkes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
Plateau S Problem For Parametric Double Integrals
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Author : Stefan Hildebrandt
language : en
Publisher:
Release Date : 2002
Plateau S Problem For Parametric Double Integrals written by Stefan Hildebrandt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Regularity For A Class Of Parametric Obstacle Problems
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Author : Fanghua Lin
language : en
Publisher:
Release Date : 1985
Regularity For A Class Of Parametric Obstacle Problems written by Fanghua Lin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Minimal Surfaces I
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Author : Ulrich Dierkes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Minimal Surfaces I written by Ulrich Dierkes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Minimal surfaces I is an introduction to the field of minimal surfaces and apresentation of the classical theory as well as of parts of the modern development centered around boundary value problems. Part II deals with the boundary behaviour of minimal surfaces. Part I is particularly apt for students who want to enter this interesting area of analysis and differential geometry which during the last 25 years of mathematical research has been very active and productive. Surveys of various subareas will lead the student to the current frontiers of knowledge and can alsobe useful to the researcher. The lecturer can easily base courses of one or two semesters on differential geometry on Vol. 1, as many topics are worked out in great detail. Numerous computer-generated illustrations of old and new minimal surfaces are included to support intuition and imagination. Part 2 leads the reader up to the regularity theory fornonlinear elliptic boundary value problems illustrated by a particular and fascinating topic. There is no comparably comprehensive treatment of the problem of boundary regularity of minimal surfaces available in book form. This long-awaited book is a timely and welcome addition to the mathematical literature.
The Problem Of Plateau
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Author : Themistocles M. Rassias
language : en
Publisher: World Scientific
Release Date : 1992
The Problem Of Plateau written by Themistocles M. Rassias and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This volume consists of papers written by eminent scientists from the international mathematical community, who present the latest information concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rad¢. The contributing papers provide insight and perspective on various problems in modern topics of Calculus of Variations, Global Differential Geometry and Global Nonlinear Analysis as related to the problem of Plateau.
Plateau S Problem And The Calculus Of Variations Mn 35
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Author : Michael Struwe
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Plateau S Problem And The Calculus Of Variations Mn 35 written by Michael Struwe and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.