The Beltrami Equation

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The Beltrami Equation

Author : Vladimir Gutlyanskii
Publisher : Springer Science & Business Media
ISBN 13 : 1461431913
Total Pages : 309 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Beltrami Equation by : Vladimir Gutlyanskii

Download or read book The Beltrami Equation written by Vladimir Gutlyanskii and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

The Beltrami Equation

Author : Tadeusz Iwaniec
Publisher : American Mathematical Soc.
ISBN 13 : 0821840452
Total Pages : 110 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Beltrami Equation by : Tadeusz Iwaniec

Download or read book The Beltrami Equation written by Tadeusz Iwaniec and published by American Mathematical Soc.. This book was released on 2008 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The measurable Riemann Mapping Theorem (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the state of the art as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.

Univalent Solutions of the Beltrami Equation

Author : Richard Marion Summerville
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.:/5 (346 download)

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Book Synopsis Univalent Solutions of the Beltrami Equation by : Richard Marion Summerville

Download or read book Univalent Solutions of the Beltrami Equation written by Richard Marion Summerville and published by . This book was released on 1969 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Quasiconformal Mappings

Author : Lars Valerian Ahlfors
Publisher : American Mathematical Soc.
ISBN 13 : 0821836447
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Quasiconformal Mappings by : Lars Valerian Ahlfors

Download or read book Lectures on Quasiconformal Mappings written by Lars Valerian Ahlfors and published by American Mathematical Soc.. This book was released on 2006-07-14 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Extending the Beltrami Equation Into Higher Dimensions

Author : Raymond K. DeCampo
Publisher :
ISBN 13 :
Total Pages : 178 pages
Book Rating : 4.:/5 (696 download)

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Book Synopsis Extending the Beltrami Equation Into Higher Dimensions by : Raymond K. DeCampo

Download or read book Extending the Beltrami Equation Into Higher Dimensions written by Raymond K. DeCampo and published by . This book was released on 1999 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Computation of the Beltrami Equation in the Complex Plane

Author : University of Minnesota. Institute for Mathematics and Its Applications
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis On the Computation of the Beltrami Equation in the Complex Plane by : University of Minnesota. Institute for Mathematics and Its Applications

Download or read book On the Computation of the Beltrami Equation in the Complex Plane written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1989 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics for Dynamic Modeling

Author : Edward Beltrami
Publisher : Academic Press
ISBN 13 : 1483267865
Total Pages : 294 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Mathematics for Dynamic Modeling by : Edward Beltrami

Download or read book Mathematics for Dynamic Modeling written by Edward Beltrami and published by Academic Press. This book was released on 2014-05-10 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48)

Author : Kari Astala
Publisher : Princeton University Press
ISBN 13 : 9780691137773
Total Pages : 708 pages
Book Rating : 4.1/5 (377 download)

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Book Synopsis Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by : Kari Astala

Download or read book Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) written by Kari Astala and published by Princeton University Press. This book was released on 2009-01-18 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

On the Regularity of Solutions to the Beltrami Equation in a Plane

Author : Bindu K. Veetel
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (932 download)

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Book Synopsis On the Regularity of Solutions to the Beltrami Equation in a Plane by : Bindu K. Veetel

Download or read book On the Regularity of Solutions to the Beltrami Equation in a Plane written by Bindu K. Veetel and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Folding Solutions of the Beltrami Equation

Author : Uri Srebro
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis On Folding Solutions of the Beltrami Equation by : Uri Srebro

Download or read book On Folding Solutions of the Beltrami Equation written by Uri Srebro and published by . This book was released on 1999 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:

When Least Is Best

Author : Paul J. Nahin
Publisher : Princeton University Press
ISBN 13 : 0691218765
Total Pages : 406 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis When Least Is Best by : Paul J. Nahin

Download or read book When Least Is Best written by Paul J. Nahin and published by Princeton University Press. This book was released on 2021-05-18 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical journey through the most fascinating problems of extremes and how to solve them What is the best way to photograph a speeding bullet? How can lost hikers find their way out of a forest? Why does light move through glass in the least amount of time possible? When Least Is Best combines the mathematical history of extrema with contemporary examples to answer these intriguing questions and more. Paul Nahin shows how life often works at the extremes—with values becoming as small (or as large) as possible—and he considers how mathematicians over the centuries, including Descartes, Fermat, and Kepler, have grappled with these problems of minima and maxima. Throughout, Nahin examines entertaining conundrums, such as how to build the shortest bridge possible between two towns, how to vary speed during a race, and how to make the perfect basketball shot. Moving from medieval writings and modern calculus to the field of optimization, the engaging and witty explorations of When Least Is Best will delight math enthusiasts everywhere.

Memoirs of the American Mathematical Society

Author :
Publisher :
ISBN 13 :
Total Pages : 974 pages
Book Rating : 4.:/5 (42 download)

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Book Synopsis Memoirs of the American Mathematical Society by :

Download or read book Memoirs of the American Mathematical Society written by and published by . This book was released on 1988 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Degenerate Beltrami Equation

Author : Vladimir Ya Gutljanskij
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (248 download)

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Book Synopsis On the Degenerate Beltrami Equation by : Vladimir Ya Gutljanskij

Download or read book On the Degenerate Beltrami Equation written by Vladimir Ya Gutljanskij and published by . This book was released on 2001 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Cahn–Hilliard Equation: Recent Advances and Applications

Author : Alain Miranville
Publisher : SIAM
ISBN 13 : 1611975921
Total Pages : 216 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Cahn–Hilliard Equation: Recent Advances and Applications by : Alain Miranville

Download or read book The Cahn–Hilliard Equation: Recent Advances and Applications written by Alain Miranville and published by SIAM. This book was released on 2019-09-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

On General Degenerate Beltrami Equation

Author : Bogdan V. Bojarski
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (254 download)

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Book Synopsis On General Degenerate Beltrami Equation by : Bogdan V. Bojarski

Download or read book On General Degenerate Beltrami Equation written by Bogdan V. Bojarski and published by . This book was released on 2008 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Morrey Spaces

Author : Yoshihiro Sawano
Publisher : CRC Press
ISBN 13 : 1000064077
Total Pages : 316 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Morrey Spaces by : Yoshihiro Sawano

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Mathematical Models for Society and Biology

Author : Edward Beltrami
Publisher : Academic Press
ISBN 13 : 0124046932
Total Pages : 281 pages
Book Rating : 4.1/5 (24 download)

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Book Synopsis Mathematical Models for Society and Biology by : Edward Beltrami

Download or read book Mathematical Models for Society and Biology written by Edward Beltrami and published by Academic Press. This book was released on 2013-06-19 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book