Existence and Partial Regularity Results for the Heat Flow for Harmonic Maps
Title | Existence and Partial Regularity Results for the Heat Flow for Harmonic Maps PDF eBook |
Author | Chen Yunmei |
Publisher | |
Pages | 28 |
Release | 1988 |
Genre | |
ISBN |
Partial Regularity for Harmonic Maps and Related Problems
Title | Partial Regularity for Harmonic Maps and Related Problems PDF eBook |
Author | Roger Moser |
Publisher | World Scientific |
Pages | 196 |
Release | 2005 |
Genre | Mathematics |
ISBN | 9812560858 |
The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.
The Analysis Of Harmonic Maps And Their Heat Flows
Title | The Analysis Of Harmonic Maps And Their Heat Flows PDF eBook |
Author | Fanghua Lin |
Publisher | World Scientific |
Pages | 280 |
Release | 2008-05-23 |
Genre | Mathematics |
ISBN | 9814472247 |
This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by Simon and Lin. The second part of the book contains a systematic coverage of heat flow of harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in higher dimensions by Lin and Wang.The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.
Partial Regularity of Heat Flows for Harmonic Maps Into Spheres
Title | Partial Regularity of Heat Flows for Harmonic Maps Into Spheres PDF eBook |
Author | Mikhail Felʹdman |
Publisher | |
Pages | 90 |
Release | 1994 |
Genre | |
ISBN |
Singular Harmonic Maps and Harmonic Heat Flow
Title | Singular Harmonic Maps and Harmonic Heat Flow PDF eBook |
Author | Adriano Pisante |
Publisher | |
Pages | 116 |
Release | 2001 |
Genre | |
ISBN |
Linear and Quasi-linear Equations of Parabolic Type
Title | Linear and Quasi-linear Equations of Parabolic Type PDF eBook |
Author | Olʹga A. Ladyženskaja |
Publisher | American Mathematical Soc. |
Pages | 74 |
Release | 1988 |
Genre | Mathematics |
ISBN | 9780821815731 |
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Nonlinear Diffusion Equations and Their Equilibrium States, 3
Title | Nonlinear Diffusion Equations and Their Equilibrium States, 3 PDF eBook |
Author | N.G Lloyd |
Publisher | Springer Science & Business Media |
Pages | 567 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461203937 |
Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.