Sharp Counter Examples in Unique Continuation for Second-order Elliptic Equations
Author : Herbert Koch
Publisher :
Page : 15 pages
File Size : 29,37 MB
Release : 2001
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ISBN :
Author : Herbert Koch
Publisher :
Page : 15 pages
File Size : 29,37 MB
Release : 2001
Category :
ISBN :
Author : Xiaoyu Fu
Publisher : Springer Nature
Page : 127 pages
File Size : 17,34 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 : Nicolas Lerner
Publisher : Springer
Page : 576 pages
File Size : 21,25 MB
Release : 2019-05-18
Category : Mathematics
ISBN : 3030159930
Over the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
Author : Murray H. Protter
Publisher :
Page : 44 pages
File Size : 18,11 MB
Release : 1959
Category : Differential equations, Elliptic
ISBN :
Author : Jose Garcia-Cuerva
Publisher : CRC Press
Page : 336 pages
File Size : 27,35 MB
Release : 2018-01-18
Category : Mathematics
ISBN : 135108058X
Contains easy access to four actual and active areas of research in Fourier Analysis and PDE Covers a wide spectrum of topics in present research Provides a complete picture of state-of-the-art methods in the field Contains 200 tables allowing the reader speedy access to precise data
Author : Feruccio Colombini
Publisher : Springer Science & Business Media
Page : 217 pages
File Size : 32,72 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461202035
The articles in this volume reflect a subsequent development after a scientific meeting entitled Carleman Estimates and Control Theory, held in Cartona in September 1999. The 14 research-level articles, written by experts, focus on new results on Carleman estimates and their applications to uniqueness and controlla bility of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, con trol theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory. the reader will find applications of Carleman estimates to stabiliza tion, observability and exact control for the wave and the SchrOdinger equations. A final paper presents a challenging list of open problems on the topic of control lability of linear and sernilinear heat equations. The papers contain exhaustive and essentially self-contained proofs directly ac cessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors are L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani. T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, and E. Zuazua.
Author :
Publisher :
Page : 520 pages
File Size : 49,8 MB
Release : 2006
Category : Mathematics
ISBN :
Author : Herbert Koch
Publisher :
Page : 26 pages
File Size : 42,24 MB
Release : 2000
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Author :
Publisher : ScholarlyEditions
Page : 1318 pages
File Size : 17,46 MB
Release : 2012-01-09
Category : Computers
ISBN : 146496453X
Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author :
Publisher :
Page : 558 pages
File Size : 44,74 MB
Release : 2006
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ISBN :