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Fully Nonlinear Pdes In Real And Complex Geometry And Optics
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Book Synopsis Fully Nonlinear PDEs in Real and Complex Geometry and Optics by : Luca Capogna
Download or read book Fully Nonlinear PDEs in Real and Complex Geometry and Optics written by Luca Capogna and published by Springer. This book was released on 2013-10-07 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this CIME summer school was to present current areas of research arising both in the theoretical and applied setting that involve fully nonlinear partial different equations. The equations presented in the school stem from the fields of Conformal Mapping Theory, Differential Geometry, Optics, and Geometric Theory of Several Complex Variables. The school consisted of four courses: Extremal problems for quasiconformal mappings in space by Luca Capogna, Fully nonlinear equations in geometry by Pengfei Guan, Monge-Ampere type equations and geometric optics by Cristian E. Gutiérrez, and On the Levi Monge Ampere equation by Annamaria Montanari.
Book Synopsis The Golden Anniversary Celebration of the National Association of Mathematicians by : Omayra Ortega
Download or read book The Golden Anniversary Celebration of the National Association of Mathematicians written by Omayra Ortega and published by American Mathematical Soc.. This book was released on 2020-12-10 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is put together by the National Association of Mathematicians to commemorate its 50th anniversary. The articles in the book are based on lectures presented at several events at the Joint Mathematics Meeting held from January 16–19, 2019, in Baltimore, Maryland, including the Claytor-Woodard Lecture as well as the NAM David Harold Blackwell Lecture, which was held on August 2, 2019, in Cincinnati, Ohio.
Book Synopsis Mathematical Methods in Liquid Crystal Optics and Lens Design by : Eric Stachura
Download or read book Mathematical Methods in Liquid Crystal Optics and Lens Design written by Eric Stachura and published by Springer Nature. This book was released on with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fully Nonlinear Pdes in Real and Complex Geometry and Optics by : Luca Capogna
Download or read book Fully Nonlinear Pdes in Real and Complex Geometry and Optics written by Luca Capogna and published by . This book was released on 2013-10-31 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Nonlinear Elliptic Equations and Nonassociative Algebras by : Nikolai Nadirashvili
Download or read book Nonlinear Elliptic Equations and Nonassociative Algebras written by Nikolai Nadirashvili and published by American Mathematical Soc.. This book was released on 2014-12-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.
Book Synopsis Geometry in Partial Differential Equations by : Agostino Prastaro
Download or read book Geometry in Partial Differential Equations written by Agostino Prastaro and published by World Scientific. This book was released on 1994 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes the interdisciplinary interaction in problems involving geometry and partial differential equations. It provides an attempt to follow certain threads that interconnect various approaches in the geometric applications and influence of partial differential equations. A few such approaches include: Morse-Palais-Smale theory in global variational calculus, general methods to obtain conservation laws for PDEs, structural investigation for the understanding of the meaning of quantum geometry in PDEs, extensions to super PDEs (formulated in the category of supermanifolds) of the geometrical methods just introduced for PDEs and the harmonic theory which proved to be very important especially after the appearance of the Atiyah-Singer index theorem, which provides a link between geometry and topology.
Download or read book Optical Engineering written by and published by . This book was released on 1991 with total page 1236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes papers reporting on research and development in optical science and engineering and the practical applications of known optical science, engineering, and technology.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1965 with total page 958 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book STAR written by and published by . This book was released on 1973 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis and Partial Differential Equations by : Alberto P. Calderón
Download or read book Harmonic Analysis and Partial Differential Equations written by Alberto P. Calderón and published by University of Chicago Press. This book was released on 1999 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alberto P. Calderón (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partial differential equations and from signal processing to tomography. In addition, he helped define the "Chicago school" of analysis, which remains influential to this day. In 1996, more than 300 mathematicians from around the world gathered in Chicago for a conference on harmonic analysis and partial differential equations held in Calderón's honor. This volume originated in papers given there and presents timely syntheses of several major fields of mathematics as well as original research articles contributed by some of the finest scholars working in these areas. An important addition to the literature, this book is essential reading for researchers in these and other related fields.
Book Synopsis Web Theory and Related Topics by : J. Grifone
Download or read book Web Theory and Related Topics written by J. Grifone and published by World Scientific. This book was released on 2001 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of recent developments in web theory. Webs (i.e. families of foliations in general position) appear in many different fields of mathematics (differential geometry, algebraic geometry, differential equations, symplectic geometry, etc.) and physics (mechanics, geometrical optics, etc.). After giving a survey on webs in differential geometry and algebraic geometry, the book presents new results on partial differential equations, integrable systems, holomorphic dynamics and nonlinear optics obtained through web theory. Contents: A Na-ve Guide to Web Geometry (I Nakai); An Introduction to Web Geometry: Analytic Web Geometry (A H(r)naut); Webs and Curvature (P T Nagy); Recent Developments: Conformal Flows on ?,0 and Hexagonal 3-Webs (M Belliart et al.); Rigidity of Webs (J-P Dufour); Resonant Geometric Optics and Webs (J-L Joly et al.); Introduction to G -Structures via Three Examples (J M Landsberg); Web Geometry and the Equivalence Problem of the First Order Partial Differential Equations (I Nakai); Veronese Webs and Transversally Veronese Foliations (M-H Rigal); A Three-Dimensional Lagrangian Four-Web with No Abelian Relation (G F Robert). Readership: Researchers and graduate students in mathematics and physics."
Author :Cristian E. Gutierrez Publisher :Springer Science & Business Media ISBN 13 :9780817641771 Total Pages :148 pages Book Rating :4.6/5 (417 download)
Book Synopsis The Monge—Ampère Equation by : Cristian E. Gutierrez
Download or read book The Monge—Ampère Equation written by Cristian E. Gutierrez and published by Springer Science & Business Media. This book was released on 2001-05-11 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monge-Ampère equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics. Monge-Ampère type equations have applications in the areas of differential geometry, the calculus of variations, and several optimization problems, such as the Monge-Kantorovitch mass transfer problem. This book stresses the geometric aspects of this beautiful theory, using techniques from harmonic analysis – covering lemmas and set decompositions.
Book Synopsis Algebraic Approaches to Partial Differential Equations by : Xiaoping Xu
Download or read book Algebraic Approaches to Partial Differential Equations written by Xiaoping Xu and published by Springer Science & Business Media. This book was released on 2013-04-23 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac equations, the KdV equation, the KP equation, the nonlinear Schrodinger equation, the Davey and Stewartson equations, the Boussinesq equations in geophysics, the Navier-Stokes equations and the boundary layer problems. In order to solve them, I have employed the grading technique, matrix differential operators, stable-range of nonlinear terms, moving frames, asymmetric assumptions, symmetry transformations, linearization techniques and special functions. The book is self-contained and requires only a minimal understanding of calculus and linear algebra, making it accessible to a broad audience in the fields of mathematics, the sciences and engineering. Readers may find the exact solutions and mathematical skills needed in their own research.
Book Synopsis Hyperbolic Partial Differential Equations and Geometric Optics by : Jeffrey Rauch
Download or read book Hyperbolic Partial Differential Equations and Geometric Optics written by Jeffrey Rauch and published by American Mathematical Soc.. This book was released on 2012-05-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.
Book Synopsis Calendar by : Chinese University of Hong Kong
Download or read book Calendar written by Chinese University of Hong Kong and published by . This book was released on 1999 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Nonlinear Partial Differential Equations by : Andrei D. Polyanin
Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
