Analytic Partial Differential Equations

Part 1. Distributions and Analyticity in Euclidean Space.- Chapter 1. Functions and Differential Operators in Euclidean Space.- Chapter 2. Distributions in Euclidean Space.- Chapter 3. Analytic Tools in Distribution Theory.- Chapter 4. Analyticity of Solutions of Linear PDEs. Basic Results.- Chapter 5. The Cauchy-Kovalevskaya Theorem.- Part 2. Hyperfunctions in Euclidean Space.- Chapter 6. Analytic Functionals in Euclidean Space.- Chapter 7. Hyperfunctions in Euclidean Space.- Chapter 8. Hyperdifferential Operators.- Part 3. Geometric Background.- Chapter 9. Elements of Differential Geometry.- Chapter 10. A Primer on Sheaf Cohomology.- Chapter 11. Distributions and Hyperfunctions on a Manifold.- Chapter 12. Lie Algebras of Vector Fields.- Chapter 13. Elements of Symplectic Geometry.- Part 4. Stratification of Analytic Varieties and Division of Distributions by Analytic Functions.- Chapter 14. Analytic Stratifications.- Chapter 15. Division of Distributions by Analytic Functions.- Part5. Analytic Pseudodifferential Operators and Fourier Integral Operators.- Chapter 16. Elementary Pseudodifferential Calculus in the $C^1$ Class.- Chapter 17. Analytic Pseudodifferential Calculus.- Chapter 18. Fourier Integral Operators.- Part 6. Complex Microlocal Analysis.- Chapter 19. Classical Analytic Formalism.- Chapter 20. Germ Fourier Integral Operators in Complex Space.- Chapter 21. Germ Pseudodifferential Operators in Complex Space.- Chapter 22. Germ FBI Transforms.- Part 7. Analytic Pseudodifferential Operators of Principal Type.- Chapter 23. Analytic PDEs of Principal Type. Local Solvability.- Chapter 24. Analytic PDEs of Principal Type. Regularity of the Solutions.- Chapter 25. Solvability of Constant Vector Fields of Type (1,0).- Chapter 26. Pseudodifferential Solvability and Property $(\Psi)$.- Chapter 27. Poincare Lemma in Pseudodifferential Tube Structures.- Index.- Bibliography.

Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.

• Análise funcional e transforma
• Cálculo diferencial e equações

partial differential equations;analytic partial differential equations;distribution;microlocal analysis;hyperfunctions;Ovsyannikov analyticity;FBI transform;analytic wave-front set;pseudodifferential operators;Fourier integral operators;partial differential equations of principal type;differential complexes;phase-functions;Cauchy-Kovalevskaya Theorem;Lojaciewicz inequality;stratification;Nagano foliations;eikonal equations;regularity of hyperfunction solutions