Download or read book On the Reflection Principle for Polyharmonic Functions written by Alfred Huber and published by . This book was released on 1955 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical reflection principle of H. A. Schwarz for harmonic functions is extended to the case of polyharmonic functions. As an application a Phragm©Øen-Lindel©·of type theorem is obtained for this class of functions.
Download or read book On Certain Reflection Principles written by Ernest P. Miles (Jr.) and published by . This book was released on 1958 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Huber recently established a reflection principle for functions polyharmonic of order p, applicable when the function and its first p-1 derivatives with respect to x1 = 0. His theorem includes as special cases the classical principle of H.A. Schwarz for harmonic functions and the corresponding results of H. Poritsky and R.J. Duffin for biharmonics. Assuming that a polyharmonic function of order p, meeting the above conditions on its derivatives, has an analytic continuation across this hyperplane, a locally valid expansion for the function is obtained in terms of its Caucy data on the hyperplane. From this expansion an alternate reflection principle of limited range is obtained which is shown to be reducible to the Schwarz, Duffin, Huber principles for p = 1, 2, 3, respectively, within their common range of validity. Results for the iterated Laplace Equation are used which closely parallel those recently discussed by the author in AFOSR TN 58-340 of April, 1958. The paper closes with a brief description of a corresponding heuristic approach to the reflection principle for the Helmholtz equation treated recently Diaz and Ludford. These results are to be presented at the Cambridge Meeting of the AMS, August 26, 1958.
Download or read book A Note on the Reflection Principle for Harmonic Functions written by D. H. Armitage and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Remarks on the Reflection Principle for Harmonic Functions written by Dmitry Khavinson and published by . This book was released on 1989 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Certain Reflection Principles written by Ernest P. Miles (Jr.) and published by . This book was released on 1958 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Huber recently established a reflection principle for functions polyharmonic of order p, applicable when the function and its first p-1 derivatives with respect to x1 = 0. His theorem includes as special cases the classical principle of H. A. Schwarz for harmonic functions and the corresponding results of H. Poritsky and R. J. Duffin for biharmonics. Assuming that a polyharmonic function of order p, meeting the above conditions on its derivatives, has an analytic continuation across this hyperplane, a locally valid expansion for the function is obtained in terms of its Caucy data on the hyperplane. From this expansion an alternate reflection principle of limited range is obtained which is shown to be reducible to the Schwarz, Duffin, Huber principles for p = 1, 2, 3, respectively, within their common range of validity. Results for the iterated Laplace Equation are used which closely parallel those recently discussed by the author in AFOSR TN 58-340 of April, 1958. The paper closes with a brief description of a corresponding heuristic approach to the reflection principle for the Helmholtz equation treated recently Diaz and Ludford. These results are to be presented at the Cambridge Meeting of the AMS, August 26, 1958.
Download or read book Polyharmonic Boundary Value Problems written by Filippo Gazzola and published by Springer. This book was released on 2010-05-26 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.
Download or read book A Note on the Reflection Principle for Harmonic Functions written by D. H. Armitage and published by . This book was released on 1976 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polyharmonic Functions written by Nachman Aronszajn and published by Oxford University Press, USA. This book was released on 1983 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Holomorphic Partial Differential Equations and Classical Potential Theory written by Dmitry Khavinson and published by American Mathematical Soc.. This book was released on 2018-07-09 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why do solutions of linear analytic PDE suddenly break down? What is the source of these mysterious singularities, and how do they propagate? Is there a mean value property for harmonic functions in ellipsoids similar to that for balls? Is there a reflection principle for harmonic functions in higher dimensions similar to the Schwarz reflection principle in the plane? How far outside of their natural domains can solutions of the Dirichlet problem be extended? Where do the continued solutions become singular and why? This book invites graduate students and young analysts to explore these and many other intriguing questions that lead to beautiful results illustrating a nice interplay between parts of modern analysis and themes in “physical” mathematics of the nineteenth century. To make the book accessible to a wide audience including students, the authors do not assume expertise in the theory of holomorphic PDE, and most of the book is accessible to anyone familiar with multivariable calculus and some basics in complex analysis and differential equations.
Download or read book AFOSR written by United States. Air Force. Office of Scientific Research and published by . This book was released on 1950 with total page 1190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Collected Papers written by Fritz John and published by . This book was released on 1985 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reflection Principles for Solutions of Equations in Elasticity written by James Henry Bramble and published by . This book was released on 1957 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper establishes certain reflection principles (analogous to the classical Schwarz reflection principle for harmonic functions) for biharmonic functions which arise as solutions of equations in elasticity.
Download or read book The Analysis of Solutions of Elliptic Equations written by Nikolai Tarkhanov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a continuation of my book "Parametrix Method in the Theory of Differential Complexes" (see [291]). There, we considered complexes of differential operators between sections of vector bundles and we strived more than for details. Although there are many applications to for maximal generality overdetermined systems, such an approach left me with a certain feeling of dissat- faction, especially since a large number of interesting consequences can be obtained without a great effort. The present book is conceived as an attempt to shed some light on these new applications. We consider, as a rule, differential operators having a simple structure on open subsets of Rn. Currently, this area is not being investigated very actively, possibly because it is already very highly developed actively (cf. for example the book of Palamodov [213]). However, even in this (well studied) situation the general ideas from [291] allow us to obtain new results in the qualitative theory of differential equations and frequently in definitive form. The greater part of the material presented is related to applications of the L- rent series for a solution of a system of differential equations, which is a convenient way of writing the Green formula. The culminating application is an analog of the theorem of Vitushkin [303] for uniform and mean approximation by solutions of an elliptic system. Somewhat afield are several questions on ill-posedness, but the parametrix method enables us to obtain here a series of hitherto unknown facts.
Download or read book Mathematics and Computing written by Ram N. Mohapatra and published by Springer. This book was released on 2015-06-25 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computing are of vital importance to a broad range of communities, including mathematicians and computing professionals across different educational levels and disciplines. In current research, modeling and simulation, making decisions under uncertainty and pattern recognition have become very common. Professionals across different educational levels and disciplines need exposure to advances in mathematics and computing. In this context, this book presents research papers on applicable areas of current interest. It also includes papers in which experts summarize research findings, such as signal processing and analysis and low-rank-matrix approximation for solving large systems, which will emerge as powerful tools for further research. These new advances and cutting-edge research in the fields of mathematics and their applications to computing are of paramount importance for young researchers.
Download or read book Pseudo Differential Operators Complex Analysis and Partial Differential Equations written by Bert-Wolfgang Schulze and published by Springer Science & Business Media. This book was released on 2010-03-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1976 with total page 1294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Aeronautical Engineering Review written by and published by . This book was released on 1957 with total page 1908 pages. Available in PDF, EPUB and Kindle. Book excerpt:
