Sergio Vessella: Unique Continuation Properties for Partial Differential Equations, Gebunden

Klappentext

• 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.