LEADER 03363nam 2200541 450 001 9910480524503321 005 20170822144314.0 010 $a1-4704-0396-X 035 $a(CKB)3360000000464982 035 $a(EBL)3114424 035 $a(SSID)ssj0000973250 035 $a(PQKBManifestationID)11602788 035 $a(PQKBTitleCode)TC0000973250 035 $a(PQKBWorkID)10958536 035 $a(PQKB)11288095 035 $a(MiAaPQ)EBC3114424 035 $a(PPN)195416856 035 $a(EXLCZ)993360000000464982 100 $a20150416h20042004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClassification and probabilistic representation of the positive solutions of a semilinear elliptic equation /$fBenoi?t Mselati 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2004. 210 4$dİ2004 215 $a1 online resource (146 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 168, Number 798 300 $a"March 2004, Volume 168, Number 798 (third of 4 numbers)." 311 $a0-8218-3509-2 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Introduction and statement of the results""; ""Chapter 1. An analytic approach to the equation I??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 I??u = u[sup(2)]""; ""Chapter 2. A probabilistic approach to the equation I??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"" 327 $a""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 I??u = u[sup(2)] in a domain""; ""5.1. Representation of solutions""; ""5.2. Admissible traces and classification results"" 327 $a""Appendix A. Technical results""""A.1. Parametrization near the boundary""; ""A.2. Estimates for the Green function""; ""A.3. The auxiliary function p""; ""A.4. Proof of Lemma 2.20""; ""Appendix. Bibliography""; ""Notation index""; ""Subject index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""P""; ""R""; ""S""; ""T"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 168, Number 798. 606 $aDifferential equations, Elliptic 608 $aElectronic books. 615 0$aDifferential equations, Elliptic. 676 $a515/.353 700 $aMselati$b Benoi?t$f1977-$0932210 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480524503321 996 $aClassification and probabilistic representation of the positive solutions of a semilinear elliptic equation$92097241 997 $aUNINA