03389nam 2200565 450 991081727390332120170822144126.00-8218-8750-5(CKB)3360000000464079(EBL)3114368(SSID)ssj0000889107(PQKBManifestationID)11488387(PQKBTitleCode)TC0000889107(PQKBWorkID)10875526(PQKB)11756366(MiAaPQ)EBC3114368(RPAM)17132077(PPN)195419081(EXLCZ)99336000000046407920150416h20112011 uy 0engur|n|---|||||txtccrOn first and second order planar elliptic equations with degeneracies /Abdelhamid MezianiProvidence, Rhode Island :American Mathematical Society,2011.©20111 online resource (77 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 217, Number 1019"May 2012, Volume 217, Number 1019 (first of 4 numbers)."0-8218-5312-0 Includes bibliographical references.""Contents""; ""Introduction""; ""Chapter 1. Preliminaries""; ""Chapter 2. Basic Solutions""; ""2.1. Properties of basic solutions""; ""2.2. The spectral equation and Spec(L0)""; ""2.3. Existence of basic solutions""; ""2.4. Properties of the fundamental matrix of (E,)""; ""2.5. The system of equations for the adjoint operator L*""; ""2.6. Continuation of a simple spectral value""; ""2.7. Continuation of a double spectral value""; ""2.8. Purely imaginary spectral value""; ""2.9. Main result about basic solutions""; ""Chapter 3. Example""""Chapter 4. Asymptotic behavior of the basic solutions of L""""4.1. Estimate of ""; ""4.2. First estimate of and ""; ""4.3. End of the proof of Theorem 4.1""; ""Chapter 5. The kernels""; ""5.1. Two lemmas""; ""5.2. Proof of Theorem 5.1""; ""5.3. Modified kernels""; ""Chapter 6. The homogeneous equation L u=0""; ""6.1. Representation of solutions in a cylinder""; ""6.2. Cauchy integral formula""; ""6.3. Consequences""; ""Chapter 7. The nonhomogeneous equation L u=F""; ""7.1. Generalized Cauchy Integral Formula""; ""7.2. The integral operator T""; ""7.3. Compactness of the operator T""""Chapter 8. The semilinear equation""""Chapter 9. The second order equation: Reduction""; ""Chapter 10. The homogeneous equation Pu=0""; ""10.1. Some properties""; ""10.2. Main result about the homogeneous equation Pu=0""; ""10.3. A maximum principle""; ""Chapter 11. The nonhomogeneous equation Pu=F""; ""Chapter 12. Normalization of a Class of Second Order Equations with a Singularity ""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 217, Number 1019.Degenerate differential equationsDifferential equations, EllipticDegenerate differential equations.Differential equations, Elliptic.515/.3533Meziani Abdelhamid1957-1714675MiAaPQMiAaPQMiAaPQBOOK9910817273903321On first and second order planar elliptic equations with degeneracies4108707UNINA