Geometric Measure Theory And Free Boundary Problems
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Geometric Measure Theory And Free Boundary Problems
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Author : Guido De Philippis
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Geometric Measure Theory And Free Boundary Problems written by Guido De Philippis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
Optimal Stopping And Free Boundary Problems
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Author : Goran Peskir
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-10
Optimal Stopping And Free Boundary Problems written by Goran Peskir 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 2006-11-10 with Mathematics categories.
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.
Shapes And Geometries
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Author : Michel C. Delfour
language : en
Publisher: SIAM
Release Date : 2001-01-01
Shapes And Geometries written by Michel C. Delfour and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
The tools to use for problems where the modeling, optimization, or control variable is the structure of a geometric object.
Isoperimetric Inequalities In Riemannian Manifolds
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Author : Manuel Ritoré
language : en
Publisher: Springer Nature
Release Date : 2023-10-06
Isoperimetric Inequalities In Riemannian Manifolds written by Manuel Ritoré and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Mathematics categories.
This work gives a coherent introduction to isoperimetric inequalities in Riemannian manifolds, featuring many of the results obtained during the last 25 years and discussing different techniques in the area. Written in a clear and appealing style, the book includes sufficient introductory material, making it also accessible to graduate students. It will be of interest to researchers working on geometric inequalities either from a geometric or analytic point of view, but also to those interested in applying the described techniques to their field.
Shapes And Geometries
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Author : M. C. Delfour
language : en
Publisher: SIAM
Release Date : 2011-01-01
Shapes And Geometries written by M. C. Delfour and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.
Geometric Measure Theory
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Author : Frank Morgan
language : en
Publisher: Elsevier
Release Date : 2000-08-22
Geometric Measure Theory written by Frank Morgan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-22 with Mathematics categories.
Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology.This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.
On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature
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Author : Man Chun Li
language : en
Publisher: Stanford University
Release Date : 2011
On A Free Boundary Problem For Embedded Minimal Surfaces And Instability Theorems For Manifolds With Positive Isotropic Curvature written by Man Chun Li and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
In this thesis, we describe a min-max construction of embedded minimal surfaces satisfying the free boundary condition in any compact 3-manifolds with boundary. We also prove the instability of minimal surfaces of certain conformal type in 4- manifolds with positive isotropic curvature. Given a compact 3-manifold M with boundary [d̳]M, consider the problem of find- ing an embedded minimal surface [Sigma] which meets [d̳]M orthogonally along [d̳][Sigma]. These surfaces are critical points to the area functional with respect to variations preserving [delta]M. We will use a min-max construction to construct such a free boundary solution and prove the regularity of such solution up to the free boundary. An interesting point is that no convexity assumption on [d̳]M is required. We also discuss some geometric properties, genus bounds for example, for these free boundary solutions. Just as positive sectional curvature tends to make geodesics unstable, positive isotropic curvature tends to make minimal surfaces unstable. In the second part of this thesis, we prove a similar instability result in dimension 4. Given a compact 4- manifold M with positive isotropic curvature, we show that any complete immersed minimal surface [Sigma] in M which is uniformly conformally equivalent to the complex plane is unstable. The same conclusion holds in higher dimensions as well if we assume that the manifold has uniformly positive complex sectional curvature. The proof uses the H ̈ormander's weighted L^2 method and the stability inequality to derive a contradiction.
Partial Differential Equations And Calculus Of Variations
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Author : Stefan Hildebrandt
language : en
Publisher: Springer
Release Date : 2006-11-14
Partial Differential Equations And Calculus Of Variations written by Stefan Hildebrandt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This volume contains 18 invited papers by members and guests of the former Sonderforschungsbereich in Bonn (SFB 72) who, over the years, collaborated on the research group "Solution of PDE's and Calculus of Variations". The emphasis is on existence and regularity results, on special equations of mathematical physics and on scattering theory.
Regularity Of Free Boundaries In Obstacle Type Problems
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Author : Arshak Petrosyan
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Regularity Of Free Boundaries In Obstacle Type Problems written by Arshak Petrosyan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.
Models Of Phase Transitions
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Author : Augusto Visintin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Models Of Phase Transitions written by Augusto Visintin 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 2012-12-06 with Mathematics categories.
... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX