On the Unique Continuation Problem of Elliptic Partial Differential Equations
Author : Irwin Stanley Bernstein
Publisher :
Page : 96 pages
File Size : 39,78 MB
Release : 1959
Category :
ISBN :
Author : Irwin Stanley Bernstein
Publisher :
Page : 96 pages
File Size : 39,78 MB
Release : 1959
Category :
ISBN :
Author : Roger Noel Pederson
Publisher :
Page : 92 pages
File Size : 23,62 MB
Release : 1957
Category : Differential equations, Partial
ISBN :
Author : Chrisopher B. Croke
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 34,78 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468493752
This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title. We would like to thank Christopher B. Croke (University of Penn sylva nia), Irena Lasiecka (University of Virginia), Gunther Uhlmann (University of Washington), and Michael S. Vogelius (Rutgers University) for their ex cellent work as organizers of the two-week summer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a selected number of articles based on lectures delivered at the IMA 2001 Summer Program on "Geometric Methods in Inverse Problems and PDE Control. " The focus of this program was some common techniques used in the study of inverse coefficient problems and control problems for partial differential equations, with particular emphasis on their strong relation to fundamental problems of geometry. Inverse coef ficient problems for partial differential equations arise in many application areas, for instance in medical imaging, nondestructive testing, and geophys ical prospecting. Control problems involving partial differential equations may arise from the need to optimize a given performance criterion, e. g. , to dampen out undesirable vibrations of a structure , or more generally, to obtain a prescribed behaviour of the dynamics.
Author :
Publisher :
Page : 0 pages
File Size : 46,96 MB
Release : 2022
Category :
ISBN :
Author : Lipman Bers
Publisher : American Mathematical Soc.
Page : 372 pages
File Size : 48,83 MB
Release : 1964-12-31
Category : Differential equations, Partial
ISBN : 9780821896983
This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.
Author : Xiaoyu Fu
Publisher : Springer Nature
Page : 127 pages
File Size : 12,95 MB
Release : 2019-10-31
Category : Mathematics
ISBN : 3030295303
This book provides a brief, self-contained introduction to Carleman estimates for three typical second order partial differential equations, namely elliptic, parabolic, and hyperbolic equations, and their typical applications in control, unique continuation, and inverse problems. There are three particularly important and novel features of the book. First, only some basic calculus is needed in order to obtain the main results presented, though some elementary knowledge of functional analysis and partial differential equations will be helpful in understanding them. Second, all Carleman estimates in the book are derived from a fundamental identity for a second order partial differential operator; the only difference is the choice of weight functions. Third, only rather weak smoothness and/or integrability conditions are needed for the coefficients appearing in the equations. Carleman Estimates for Second Order Partial Differential Operators and Applications will be of interest to all researchers in the field.
Author : L. E. Payne
Publisher : SIAM
Page : 81 pages
File Size : 11,42 MB
Release : 1975-06-01
Category : Mathematics
ISBN : 0898710197
A discussion of improperly posed Cauchy problems in partial differential equations
Author : Murray H. Protter
Publisher :
Page : 44 pages
File Size : 24,92 MB
Release : 1959
Category : Differential equations, Elliptic
ISBN :
Author : D. Gilbarg
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 37,7 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 364296379X
This volume is intended as an essentially self contained exposition of portions of the theory of second order quasilinear elliptic partial differential equations, with emphasis on the Dirichlet problem in bounded domains. It grew out of lecture notes for graduate courses by the authors at Stanford University, the final material extending well beyond the scope of these courses. By including preparatory chapters on topics such as potential theory and functional analysis, we have attempted to make the work accessible to a broad spectrum of readers. Above all, we hope the readers of this book will gain an appreciation of the multitude of ingenious barehanded techniques that have been developed in the study of elliptic equations and have become part of the repertoire of analysis. Many individuals have assisted us during the evolution of this work over the past several years. In particular, we are grateful for the valuable discussions with L. M. Simon and his contributions in Sections 15.4 to 15.8; for the helpful comments and corrections of J. M. Cross, A. S. Geue, J. Nash, P. Trudinger and B. Turkington; for the contributions of G. Williams in Section 10.5 and of A. S. Geue in Section 10.6; and for the impeccably typed manuscript which resulted from the dedicated efforts oflsolde Field at Stanford and Anna Zalucki at Canberra. The research of the authors connected with this volume was supported in part by the National Science Foundation.
Author : Michel Chipot
Publisher : Springer Nature
Page : 393 pages
File Size : 43,91 MB
Release :
Category :
ISBN : 3031541235