Bernoulli free-boundary problems / / E. Shargorodsky, J.F. Toland

• Record Nr.: UNINA9910788852903321
• Autore: Shargorodsky E (Eugene), <1966->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2008]; ©2008
• ISBN: 1-4704-0520-2
• Descrizione fisica: 1 online resource (86 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 914
• Disciplina: 515/.35
• Soggetti: Nonlinear boundary value problems; Fluid mechanics; Pseudodifferential operators
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "November 2008, volume 195, number 914 (first of 5 numbers )."
• Nota di bibliografia: Includes bibliographical references (pages 65-67) and index.
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Bernoulli Free Boundaries""; ""2.1. Special case: steady hydrodynamic waves""; ""2.2. General Case""; ""2.3. Notation""; ""2.4. Formulation as a Single Equation""; ""2.5. Equations""; ""2.6. Example of (2.7) with Explicit Solutions""; ""2.7. Equivalence""; ""2.8. Inequalities""; ""2.9. Duality""; ""2.10. Example of (2.7) with Explicit Solutions: Duality""; ""2.11. Self-duality""; ""Chapter 3. Type-(I) Problems""; ""3.1. Regularity""; ""3.2. Example of (2.7) with Explicit Solutions: Regularity""; ""3.3. Dimension of the Set of Stagnation Points""""3.4. Jordan Curves""; ""3.5. Example of (2.7) with Explicit Solutions: Jordan Curves""; ""3.6. Nekrasov's Equation""; ""3.7. Nekrasov Duality""; ""3.8. Example of (2.7) with Explicit Solutions: Nekrasov Duality""; ""3.9. Morse Index of Non-singular Solutions""; ""3.10. Example of (2.7) with Explicit Solutions: Morse Index""; ""3.11. Stokes Waves""; ""Chapter 4. Proofs of Main Results""; ""4.1. Equations: proofs of Theorem 2.4 and Corollary 2.5""; ""4.2. Equivalence: proofs of Theorems 2.7, 2.8 and 2.9""; ""4.3. Inequalities: proof of Theorem 2.10""""4.4. Duality""; ""4.5. Regularity: proofs of Theorems 3.1 and 3.3""; ""4.6. Dimension of the Set of Stagnation Points: proof of Theorem 3.4""; ""4.7. Jordan Curves: proofs of Theorem 3.5 and (3.3)""; ""4.8. Nekrasov's Equation: proof of Theorem 3.8""; ""4.9. Morse Indices""; ""4.10. Plotnikov's ; Transformation""; ""4.11. Sign of the Plotnikov Potential""; ""4.12. Constant Plotnikov Potentials: Proofs of Theorem 3.14""; ""4.13. Simple Morse-Index Estimates: Proof of Lemma 3.10""; ""4.14. Morse Index and Stagnation Points""; ""4.15. Proof of Theorem 3.13""""Appendix A. Auxiliary results""; ""Bibliography""; ""Index""