03363nam 2200541 450 991048052450332120170822144314.01-4704-0396-X(CKB)3360000000464982(EBL)3114424(SSID)ssj0000973250(PQKBManifestationID)11602788(PQKBTitleCode)TC0000973250(PQKBWorkID)10958536(PQKB)11288095(MiAaPQ)EBC3114424(PPN)195416856(EXLCZ)99336000000046498220150416h20042004 uy 0engur|n|---|||||txtccrClassification and probabilistic representation of the positive solutions of a semilinear elliptic equation /Benoît MselatiProvidence, Rhode Island :American Mathematical Society,2004.©20041 online resource (146 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 168, Number 798"March 2004, Volume 168, Number 798 (third of 4 numbers)."0-8218-3509-2 Includes bibliographical references and index.""Contents""; ""Introduction and statement of the results""; ""Chapter 1. An analytic approach to the equation Î?u = u[sup(2)]""; ""1.1. Parametrization near the boundary of the domain""; ""1.2. Basic facts about linear elliptic PDE's""; ""1.3. The equation Î?u = u[sup(2)]""; ""Chapter 2. A probabilistic approach to the equation Î?u = u[sup(2)]""; ""2.1. Linear elliptic PDE's and Brownian motion""; ""2.2. The Brownian snake""; ""2.3. Stochastic boundary values""; ""2.4. Fine topology and fine trace""; ""2.5. Two key problems""; ""Chapter 3. Lower bounds for solutions""""Main results proved in this chapter""""3.1. Upper bounds for u[sub(K)] in terms of the boundary capacity of K""; ""3.2. Lower bounds for cr-moderate solutions""; ""3.3. Synthesis""; ""Chapter 4. Upper bounds for solutions""; ""Main results proved in this chapter""; ""4.1. The case of a ""strongly star-shaped domain""""; ""4.2. The case of a general domain""; ""4.3. Proof of Proposition 4.1""; ""Chapter 5. The classification and representation of the solutions of Î?u = u[sup(2)] in a domain""; ""5.1. Representation of solutions""; ""5.2. Admissible traces and classification results""""Appendix A. Technical results""""A.1. Parametrization near the boundary""; ""A.2. Estimates for the Green function""; ""A.3. The auxiliary function p""; ""A.4. Proof of Lemma 2.20""; ""Appendix. Bibliography""; ""Notation index""; ""Subject index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T""Memoirs of the American Mathematical Society ;Volume 168, Number 798.Differential equations, EllipticElectronic books.Differential equations, Elliptic.515/.353Mselati Benoît1977-932210MiAaPQMiAaPQMiAaPQBOOK9910480524503321Classification and probabilistic representation of the positive solutions of a semilinear elliptic equation2097241UNINA