A General Method of Weights in the D-Bar-Neumann Problem PDF Download
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Author: Tran Vu Khanh
Publisher: LAP Lambert Academic Publishing
ISBN: 9783845402475
Category :
Languages : en
Pages : 120
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Book Description
This book studies the d-bar-Neumann problem in Several Complex Variables and especially focuses on a general estimate on domains which are not necessarily of D'Angelo finite type and pseudoconvexity. When the domain is pseudoconvex and of finite type, a great deal of work has been done on subelliptic estimates. The most general results concerning this problem have been obtained by J.J. Kohn in his Acta Mathematica paper in 1979 and by D. Catlin in his Annals of Mathematics paper in 1983. We use the method of weights of D. Catlin to study this problem on domains of the general type.
Author: Tran Vu Khanh
Publisher: LAP Lambert Academic Publishing
ISBN: 9783845402475
Category :
Languages : en
Pages : 120
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Book Description
This book studies the d-bar-Neumann problem in Several Complex Variables and especially focuses on a general estimate on domains which are not necessarily of D'Angelo finite type and pseudoconvexity. When the domain is pseudoconvex and of finite type, a great deal of work has been done on subelliptic estimates. The most general results concerning this problem have been obtained by J.J. Kohn in his Acta Mathematica paper in 1979 and by D. Catlin in his Annals of Mathematics paper in 1983. We use the method of weights of D. Catlin to study this problem on domains of the general type.
Author: Khanh Tran Vu
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Friedrich Haslinger
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110377837
Category : Mathematics
Languages : en
Pages : 298
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Book Description
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. It begins with results on the canonical solution operator to restricted to Bergman spaces of holomorphic d-bar functions in one and several complex variables.These operators are Hankel operators of special type. In the following the general complex is investigated on d-bar spaces over bounded pseudoconvex domains and on weighted d-bar spaces. The main part is devoted to the spectral analysis of the complex Laplacian and to compactness of the Neumann operator. The last part contains a detailed account of the application of the methods to Schrödinger operators, Pauli and Dirac operators and to Witten-Laplacians. It is assumed that the reader has a basic knowledge of complex analysis, functional analysis and topology. With minimal prerequisites required, this book provides a systematic introduction to an active area of research for both students at a bachelor level and mathematicians.
![Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem PDF](https://books.google.com/books/content/images/frontcover/OX7IaM3Cx6cC?fife=w80-h100)
Author: Emil J. Straube
Publisher: European Mathematical Society
ISBN: 9783037190760
Category : Mathematics
Languages : en
Pages : 220
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Book Description
This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.
![Lectures on the L2-Sobolev Theory of the [d-bar]-Neumann Problem PDF](https://books.google.com/books/content/images/frontcover/byXDJ3LGSFYC?fife=w80-h100)
Author: Emil J. Straube
Publisher: European Mathematical Society
ISBN: 3037190760
Category : Mathematics
Languages : en
Pages : 1
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Book Description
This book provides a thorough and self-contained introduction to the $\bar{\partial}$-Neumann problem, leading up to current research, in the context of the $\mathcal{L}^{2}$-Sobolev theory on bounded pseudoconvex domains in $\mathbb{C}^{n}$. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A & M University. The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic $\mathcal{L}^{2}$-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research. Prerequisites are a solid background in basic complex and functional analysis, including the elementary $\mathcal{L}^{2}$-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 934
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Book Description
Author: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Author: Friedrich Haslinger
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110417243
Category : Mathematics
Languages : en
Pages : 348
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Book Description
In this textbook, a concise approach to complex analysis of one and several variables is presented. After an introduction of Cauchy‘s integral theorem general versions of Runge‘s approximation theorem and Mittag-Leffler‘s theorem are discussed. The fi rst part ends with an analytic characterization of simply connected domains. The second part is concerned with functional analytic methods: Fréchet and Hilbert spaces of holomorphic functions, the Bergman kernel, and unbounded operators on Hilbert spaces to tackle the theory of several variables, in particular the inhomogeneous Cauchy-Riemann equations and the d-bar Neumann operator. Contents Complex numbers and functions Cauchy’s Theorem and Cauchy’s formula Analytic continuation Construction and approximation of holomorphic functions Harmonic functions Several complex variables Bergman spaces The canonical solution operator to Nuclear Fréchet spaces of holomorphic functions The -complex The twisted -complex and Schrödinger operators
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 1016
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Book Description
