Elliptic partial differential equations v. 1 Fredholm theory of elliptic problems in unbounded domains

The theory of elliptic partial differential equations has developed during about two centuries together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications. It remains one of the most rapidly developing fields of mathematics. The theory of general elliptic problems is presented in the present first volume of the book. A priori estimates, normal solvability and Fredholm property, index, operators with a parameter, nonlinear Fredholm operators are discussed. Particular attention is paid to elliptic problems in unbounded domains which are not yet sufficiently well presented in the existing literature and which require some special approaches. The second volumewill be devoted to reaction-diffusion equations. Existence and bifurcations of solutions, travelling waves, spectral properties and other questions are studied in relation with numerous applications in chemical physics, biology and medicine. Systematic investigation of general elliptic problems applicable bothfor bounded and unbounded domains Focus on unbounded domains which has not been sufficiently presented in the existing literature Mostly self-contained presentation of the results INDICE: Chapter 1. Introduction.- Chapter 2. Function spaces and operators.- Chapter 3. A priori estimates.- Chapter 4. Normal solvability.- Chapter 5. Fredholm property.- Chapter 6. Formally adjoint problems.- Chapter 7. Ellipticproblems with a parameter.- Chapter 8. Index of elliptic operators.- Chapter 9. Problems in cylinders.- Chapter 10. Non-Fredholm operators.- Chapter 11. Nonlinear Fredholm operators.- Supplement. Discrete operators.-Historical and bibliographical comments.- Acknowledgements.- References.

• ISBN: 978-3-0346-0536-6
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 600
• Fecha Publicación: 31/12/2010
• Nº Volúmenes: 1
• Idioma: Inglés