Fredholm Theory of Partial Differential Equations on Complete Riemannian Manifolds
Author: Robert Colman McOwen
Publisher:
Published: 1978
Total Pages: 110
ISBN-13:
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Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Author: Alexander Grigor'yan
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2021-01-18
Total Pages: 337
ISBN-13: 3110700859
DOWNLOAD EBOOKThe book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
The Hodge-Laplacian
Author: Dorina Mitrea
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2016-10-10
Total Pages: 528
ISBN-13: 3110484382
DOWNLOAD EBOOKThe core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains. Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index
Spectral Theory of Linear Differential Operators and Comparison Algebras
Author: Heinz Otto Cordes
Publisher: Cambridge University Press
Published: 1987-04-23
Total Pages: 357
ISBN-13: 0521284430
DOWNLOAD EBOOKThe main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The author then introduces comparison algebras and describes their theory in L2-spaces and L2-Soboler spaces, and in particular their importance in solving functional analytic problems involving differential operators. The book is based on lectures given in Sweden and the USA.
Geometric Aspects of Partial Differential Equations
Author: Krzysztof Wojciechowski
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 282
ISBN-13: 0821820613
DOWNLOAD EBOOKThis collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.
A Quantum Kirwan Map: Bubbling and Fredholm Theory for Symplectic Vortices over the Plane
Author: Fabian Ziltener
Publisher: American Mathematical Soc.
Published: 2014-06-05
Total Pages: 142
ISBN-13: 0821894722
DOWNLOAD EBOOKConsider a Hamiltonian action of a compact connected Lie group on a symplectic manifold . Conjecturally, under suitable assumptions there exists a morphism of cohomological field theories from the equivariant Gromov-Witten theory of to the Gromov-Witten theory of the symplectic quotient. The morphism should be a deformation of the Kirwan map. The idea, due to D. A. Salamon, is to define such a deformation by counting gauge equivalence classes of symplectic vortices over the complex plane . The present memoir is part of a project whose goal is to make this definition rigorous. Its main results deal with the symplectically aspherical case.
Partial Differential Equations and Calculus of Variations
Author: Stefan Hildebrandt
Publisher: Springer
Published: 2006-11-14
Total Pages: 433
ISBN-13: 3540460241
DOWNLOAD EBOOKThis 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.
The Technique of Pseudodifferential Operators
Author: Heinz Otto Cordes
Publisher: Cambridge University Press
Published: 1995-02-23
Total Pages: 398
ISBN-13: 0521378648
DOWNLOAD EBOOKPseudodifferential operators arise naturally in a solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. While a pseudodifferential operator is commonly defined by an integral formula, it also may be described by invariance under action of a Lie group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution, and the relation of the hyperbolic theory to the propagation of maximal ideals. The Technique of Pseudodifferential Operators will be of particular interest to researchers in partial differential equations and mathematical physics.
Geometry of Manifolds
Author: K. Shiohama
Publisher: Elsevier
Published: 1989-10-04
Total Pages: 536
ISBN-13: 0080925782
DOWNLOAD EBOOKThis volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.
Partial Differential Equations on Manifolds
Author: Robert Everist Greene
Publisher:
Published: 1993
Total Pages: 560
ISBN-13: 9780821814932
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