Aspects of Boundary Problems in Analysis and Geometry

Aspects of Boundary Problems in Analysis and Geometry
Title Aspects of Boundary Problems in Analysis and Geometry PDF eBook
Author Juan Gil
Publisher Birkhäuser
Pages 574
Release 2012-12-06
Genre Mathematics
ISBN 3034878508

Download Aspects of Boundary Problems in Analysis and Geometry Book in PDF, Epub and Kindle

Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.

A Geometric Approach to Free Boundary Problems

A Geometric Approach to Free Boundary Problems
Title A Geometric Approach to Free Boundary Problems PDF eBook
Author Luis A. Caffarelli
Publisher American Mathematical Soc.
Pages 282
Release 2005
Genre Mathematics
ISBN 0821837842

Download A Geometric Approach to Free Boundary Problems Book in PDF, Epub and Kindle

We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

The Hodge-Laplacian

The Hodge-Laplacian
Title The Hodge-Laplacian PDF eBook
Author Dorina Mitrea
Publisher Walter de Gruyter GmbH & Co KG
Pages 528
Release 2016-10-10
Genre Mathematics
ISBN 3110484382

Download The Hodge-Laplacian Book in PDF, Epub and Kindle

The 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

Analysis and Geometry in Several Complex Variables

Analysis and Geometry in Several Complex Variables
Title Analysis and Geometry in Several Complex Variables PDF eBook
Author Gen Komatsu
Publisher Springer Science & Business Media
Pages 322
Release 2012-12-06
Genre Mathematics
ISBN 1461221668

Download Analysis and Geometry in Several Complex Variables Book in PDF, Epub and Kindle

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol ume treats various aspects of CR geometry and the Bergman kernel/ pro jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

Extension problems in complex and CR-geometry

Extension problems in complex and CR-geometry
Title Extension problems in complex and CR-geometry PDF eBook
Author Alberto Saracco
Publisher Edizioni della Normale
Pages 0
Release 2008-12-29
Genre Mathematics
ISBN 9788876423383

Download Extension problems in complex and CR-geometry Book in PDF, Epub and Kindle

This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and non-compact holes), on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem. The last two subjects include detailed results by the author on non-compact extension: the cohomology of semi q-coronae and the unbounded boundary problem.

Boundary Element Analysis

Boundary Element Analysis
Title Boundary Element Analysis PDF eBook
Author Martin Schanz
Publisher Springer Science & Business Media
Pages 360
Release 2007-04-29
Genre Technology & Engineering
ISBN 3540475338

Download Boundary Element Analysis Book in PDF, Epub and Kindle

This volume contains eleven contributions on boundary integral equation and boundary element methods. Beside some historical and more analytical aspects in the formulation and analysis of boundary integral equations, modern fast boundary element methods are also described and analyzed from a mathematical point of view. In addition, the book presents engineering and industrial applications that show the ability of boundary element methods to solve challenging problems from different fields.

Geometric Aspects of Partial Differential Equations

Geometric Aspects of Partial Differential Equations
Title Geometric Aspects of Partial Differential Equations PDF eBook
Author Krzysztof Wojciechowski
Publisher American Mathematical Soc.
Pages 282
Release 1999
Genre Mathematics
ISBN 0821820613

Download Geometric Aspects of Partial Differential Equations Book in PDF, Epub and Kindle

This 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.