Description

Book Synopsis

- 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.

Unique Continuation Properties for Partial Differential Equations

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    A Hardback by Sergio Vessella

    15 in stock


      View other formats and editions of Unique Continuation Properties for Partial Differential Equations by Sergio Vessella

      Publisher: Springer
      Publication Date: 17/05/2025
      ISBN13: 9783031863653, 978-3031863653
      ISBN10:
      Also in:
      Mathematics Calculus and mathematical analysis

      Description

      Book Synopsis

      - 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.

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