LEADER 03681nam 2200613 450 001 9910788852903321 005 20170816143332.0 010 $a1-4704-0520-2 035 $a(CKB)3360000000465098 035 $a(EBL)3114220 035 $a(SSID)ssj0000888796 035 $a(PQKBManifestationID)11525286 035 $a(PQKBTitleCode)TC0000888796 035 $a(PQKBWorkID)10865784 035 $a(PQKB)10264590 035 $a(MiAaPQ)EBC3114220 035 $a(RPAM)15358749 035 $a(PPN)195418034 035 $a(EXLCZ)993360000000465098 100 $a20080708h20082008 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBernoulli free-boundary problems /$fE. Shargorodsky, J.F. Toland 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008] 210 4$dİ2008 215 $a1 online resource (86 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 914 300 $a"November 2008, volume 195, number 914 (first of 5 numbers )." 311 $a0-8218-4189-0 320 $aIncludes bibliographical references (pages 65-67) and index. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""4.15. Proof of Theorem 3.13""""Appendix A. Auxiliary results""; ""Bibliography""; ""Index"" 410 0$aMemoirs of the American Mathematical Society ;$vno. 914. 606 $aNonlinear boundary value problems 606 $aFluid mechanics 606 $aPseudodifferential operators 615 0$aNonlinear boundary value problems. 615 0$aFluid mechanics. 615 0$aPseudodifferential operators. 676 $a515/.35 700 $aShargorodsky$b E$g(Eugene),$f1966-$01565968 702 $aToland$b John F.$f1949- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910788852903321 996 $aBernoulli free-boundary problems$93836143 997 $aUNINA