Elliptic Regularization and Partial Regularity for Motion by Mean Curvature

✍ Scribed by Tom Ilmanen

Publisher: Amer Mathematical Society
Year: 1994
Tongue: English
Leaves: 106
Series: Memoirs of the American Mathematical Society
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This monograph considers (singular) surfaces moving by mean curvature, combining tools of geometric measure theory with "viscosity solution" techniques. Employing the geometrically natural concept of "elliptic regularization", Ilmanen establishes the existence of these surfaces. The ground-breaking work of Brakke, combined with the recently developed "level-set" approach, yields surfaces moving by mean curvature that are smooth almost everywhere. The methods developed here should form a foundation for further work in the field. This book is also noteworthy for its especially clear exposition and for an introductory chapter summarizing the key compactness theorems of geometric measure theory.

📜 SIMILAR VOLUMES

Elliptic Regularization and Partial Regu

📁 Elliptic Regularization and Partial Regularity for Motion by Mean Curvature

✍ Tom Ilmanen 📂 Library 📅 1994 🏛 Amer Mathematical Society 🌐 English

Regularity theory for mean curvature flo

📁 Regularity theory for mean curvature flow

✍ Klaus Ecker 📂 Library 📅 2004 🏛 Birkhäuser Boston 🌐 English

This work is devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. Mean curvature flow and related geometric evolution equations are important tool

Regularity theory for mean curvature flo

📁 Regularity theory for mean curvature flow

✍ Klaus Ecker 📂 Library 📅 2004 🏛 Birkhäuser 🌐 English

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mat

Regularity Theory for Mean Curvature Flo

📁 Regularity Theory for Mean Curvature Flow

✍ Klaus Ecker (auth.) 📂 Library 📅 2004 🏛 Birkhäuser Basel 🌐 English

"The central theme [in this book] is the regularity theory for mean curvature flow leading to a clear simplified proof of Brakke's main regularity theorem for this special case.... [The] author gives a detailed account of techniques for the study of singularities and expresses the underlying i

Elliptic Partial Differential Equations:

📁 Elliptic Partial Differential Equations: Existence and Regularity of Distributional Solutions

✍ Lucio Boccardo; Gisella Croce 📂 Library 📅 2013 🏛 De Gruyter 🌐 English

Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional so

Fine Regularity of Solutions of Elliptic

📁 Fine Regularity of Solutions of Elliptic Partial Differential Equations

✍ Maly J., Ziemer W.P. 📂 Library 📅 1997 🏛 American Mathematical Society 🌐 English

The primary objective of this book is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second-order elliptic quasilinear equations in divergence form. The structure of these equations allows coefficients in certain