Unique Continuation Properties for Partial Differential Equations Introduction to the Stability Estimates for Inverse Problems /
This 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, functi...
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| Format: | Electronic eBook |
| Language: | English |
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Cham :
Springer Nature Switzerland : Imprint: Birkhäuser,
2025.
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| Edition: | 1st ed. 2025. |
| Series: | Birkhäuser Advanced Texts Basler Lehrbücher,
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| Online Access: | https://doi.org/10.1007/978-3-031-86366-0 |
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| 100 | 1 | |a Vessella, Sergio. |e author. |0 (orcid)0000-0003-0139-8690 |1 https://orcid.org/0000-0003-0139-8690 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Unique Continuation Properties for Partial Differential Equations |h [electronic resource] : |b Introduction to the Stability Estimates for Inverse Problems / |c by Sergio Vessella. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Birkhäuser, |c 2025. | |
| 300 | |a 1 online resource (XVI, 957 p. 26 illus.). |b 14 illus. in color. | ||
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| 490 | 1 | |a Birkhäuser Advanced Texts Basler Lehrbücher, |x 2296-4894 | |
| 505 | 0 | |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. | |
| 520 | |a This 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Mathematics. | |
| 650 | 1 | 4 | |a Analysis. |
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| 830 | 0 | |a Birkhäuser Advanced Texts Basler Lehrbücher, |x 2296-4894 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-86366-0 |
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| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||