LEADER 03859nam  22004935  450 
001 9910338246003321
005 20200705051558.0
010   $a3-030-15993-0
024 7 $a10.1007/978-3-030-15993-1
035   $a(CKB)4100000008217384
035   $a(MiAaPQ)EBC5776082
035   $a(DE-He213)978-3-030-15993-1
035   $a(PPN)236522469
035   $a(EXLCZ)994100000008217384
100   $a20190518d2019      u|         0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aCarleman Inequalities $eAn Introduction and More /$fby Nicolas Lerner
205   $a1st ed. 2019.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019.
215   $a1 online resource (577 pages)
225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v353
311   $a3-030-15992-2 
327   $a1 Prolegomena -- 2 A Toolbox for Carleman Inequalities -- 3 Operators with Simple Characteristics: Calderon's Theorems -- 4 Pseudo-convexity: Hormander's Theorems -- 5 Complex Coefficients and Principal Normality -- 6 On the Edge of Pseudo-convexity -- 7 Operators with Partially Analytic Coefficients -- 8 Strong Unique Continuation Properties for Elliptic Operators -- 9 Carleman Estimates via Brenner's Theorem and Strichartz Estimates -- 10 Elliptic Operators with Jumps; Conditional Pseudo-convexity -- 11 Perspectives and Developments -- A Elements of Fourier Analysis -- B Miscellanea -- References -- Index.
330   $aOver the past 25 years, Carleman estimates have become an essential tool in several areas related to partial differential equations such as control theory, inverse problems, or fluid mechanics. This book provides a detailed exposition of the basic techniques of Carleman Inequalities, driven by applications to various questions of unique continuation. Beginning with an elementary introduction to the topic, including examples accessible to readers without prior knowledge of advanced mathematics, the book's first five chapters contain a thorough exposition of the most classical results, such as Calderón's and Hörmander's theorems. Later chapters explore a selection of results of the last four decades around the themes of continuation for elliptic equations, with the Jerison-Kenig estimates for strong unique continuation, counterexamples to Cauchy uniqueness of Cohen and Alinhac & Baouendi, operators with partially analytic coefficients with intermediate results between Holmgren's and Hörmander's uniqueness theorems, Wolff's modification of Carleman's method, conditional pseudo-convexity, and more. With examples and special cases motivating the general theory, as well as appendices on mathematical background, this monograph provides an accessible, self-contained basic reference on the subject, including a selection of the developments of the past thirty years in unique continuation.
410  0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v353
606   $aOperator theory
606   $aPartial differential equations
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
615  0$aOperator theory.
615  0$aPartial differential equations.
615 14$aOperator Theory.
615 24$aPartial Differential Equations.
676   $a515.26
676   $a515.26
700   $aLerner$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$061544
906   $aBOOK
912   $a9910338246003321
996   $aCarleman Inequalities$91732393
997   $aUNINA