LEADER 03950nam 22005295 450 001 9910999779103321 005 20250430130234.0 010 $a3-031-86366-6 024 7 $a10.1007/978-3-031-86366-0 035 $a(CKB)38672197100041 035 $a(DE-He213)978-3-031-86366-0 035 $a(MiAaPQ)EBC32086068 035 $a(Au-PeEL)EBL32086068 035 $a(OCoLC)1523374505 035 $a(EXLCZ)9938672197100041 100 $a20250430d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aUnique Continuation Properties for Partial Differential Equations $eIntroduction to the Stability Estimates for Inverse Problems /$fby Sergio Vessella 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2025. 215 $a1 online resource (XVI, 957 p. 26 illus., 14 illus. in color.) 225 1 $aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 311 08$a3-031-86365-8 327 $a- 1. Introduction -- Part I: The Sobolev Spaces and the Boundary Value Problems -- 2. Main notations and basic formulas -- 3. Overview of measure theory and functional analysis -- 4. Notes on the distribution theory and Fourier transform -- 5. The Sobolev spaces -- 6. The boundary value problems for second?order elliptic equations and the Dirichlet to Neumann map -- Part II: Cauchy Problem for PDEs and Stability Estimates -- 7. The Cauchy problem for the first?order PDEs -- 8. Real analytic functions -- 9. The Cauchy problem for PDEs with analytic coefficients -- 10. Uniqueness for an inverse problem -- 11. The Hadamard example. Solvability of the Cauchy problem and continuous dependence by the data -- 12. Ill?posed problems. Conditional stability -- 13. The John stability Theorem for the Cauchy problem for PDEs with analytic coefficients -- Part III: Carleman Estimates and Unique Continuation Properties -- 14. Carleman estimates: a first look with simple examples and basic applications -- 15. Carleman estimates and the Cauchy problem for operators with ?? coefficients in the principal part -- 16. Carleman estimates for reduced regularity coefficients -- 17. Carleman estimates for second?order operators with real coefficients in the principal part -- 18. Optimal three sphere and doubling inequality for second?order elliptic equations -- 19. Miscellanea. 330 $aThis book provides a comprehensive and self-contained introduction to the study of the Cauchy problem and unique continuation properties for partial differential equations. Aimed at graduate and advanced undergraduate students, it bridges foundational concepts such as Lebesgue measure theory, functional analysis, and partial differential equations with advanced topics like stability estimates in inverse problems and quantitative unique continuation. By presenting detailed proofs and illustrative examples, the text equips readers with a deeper understanding of these fundamental topics and their applications in mathematical analysis. Designed to serve as both a learning resource and a reference, this book is particularly suited for those pursuing research in mathematical physics, inverse problems, or applied analysis. 410 0$aBirkhäuser Advanced Texts Basler Lehrbücher,$x2296-4894 606 $aMathematical analysis 606 $aMathematics 606 $aAnalysis 606 $aMathematics 615 0$aMathematical analysis. 615 0$aMathematics. 615 14$aAnalysis. 615 24$aMathematics. 676 $a515 700 $aVessella$b Sergio$4aut$4http://id.loc.gov/vocabulary/relators/aut$042619 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910999779103321 996 $aUnique Continuation Properties for Partial Differential Equations$94374964 997 $aUNINA