LEADER 04995nam 22010694a 450 001 9910778097803321 005 20200520144314.0 010 $a1-282-08723-1 010 $a1-282-93537-2 010 $a9786612935374 010 $a9786612087233 010 $a1-4008-2616-0 024 7 $a10.1515/9781400826162 035 $a(CKB)1000000000756335 035 $a(EBL)445417 035 $a(OCoLC)367689143 035 $a(SSID)ssj0000113336 035 $a(PQKBManifestationID)11145499 035 $a(PQKBTitleCode)TC0000113336 035 $a(PQKBWorkID)10101454 035 $a(PQKB)10728495 035 $a(DE-B1597)446346 035 $a(OCoLC)979578332 035 $a(DE-B1597)9781400826162 035 $a(Au-PeEL)EBL445417 035 $a(CaPaEBR)ebr10284256 035 $a(CaONFJC)MIL293537 035 $a(MiAaPQ)EBC445417 035 $a(PPN)17026968X 035 $a(EXLCZ)991000000000756335 100 $a20031117d2004 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBlow-up theory for elliptic PDEs in Riemannian geometry$b[electronic resource] /$fOlivier Druet, Emmanuel Hebey, Fre?de?ric Robert 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2004 215 $a1 online resource (227 p.) 225 0 $aMathematical Notes ;$v45 300 $aDescription based upon print version of record. 311 $a0-691-11953-8 320 $aIncludes bibliographical references (p. [213]-218). 327 $tFront matter --$tContents --$tPreface --$tChapter 1. Background Material --$tChapter 2. The Model Equations --$tChapter 3. Blow-up Theory in Sobolev Spaces --$tChapter 4. Exhaustion and Weak Pointwise Estimates --$tChapter 5. Asymptotics When the Energy Is of Minimal Type --$tChapter 6. Asymptotics When the Energy Is Arbitrary --$tAppendix A. The Green's Function on Compact Manifolds --$tAppendix B. Coercivity Is a Necessary Condition --$tBibliography 330 $aElliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980's. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields. 410 0$aMathematical Notes 606 $aCalculus of variations 606 $aDifferential equations, Nonlinear 606 $aGeometry, Riemannian 610 $aAsymptotic analysis. 610 $aCayley?Hamilton theorem. 610 $aContradiction. 610 $aCurvature. 610 $aDiffeomorphism. 610 $aDifferentiable manifold. 610 $aEquation. 610 $aEstimation. 610 $aEuclidean space. 610 $aLaplace's equation. 610 $aMaximum principle. 610 $aNonlinear system. 610 $aPolynomial. 610 $aPrinceton University Press. 610 $aResult. 610 $aRicci curvature. 610 $aRiemannian geometry. 610 $aRiemannian manifold. 610 $aSimply connected space. 610 $aSphere theorem (3-manifolds). 610 $aStone's theorem. 610 $aSubmanifold. 610 $aSubsequence. 610 $aTheorem. 610 $aThree-dimensional space (mathematics). 610 $aTopology. 610 $aUnit sphere. 615 0$aCalculus of variations. 615 0$aDifferential equations, Nonlinear. 615 0$aGeometry, Riemannian. 676 $a515/.353 686 $a31.45$2bcl 700 $aDruet$b Olivier$f1976-$01542996 701 $aHebey$b Emmanuel$f1964-$061069 701 $aRobert$b Fre?de?ric$f1974-$01576416 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778097803321 996 $aBlow-up theory for elliptic PDEs in Riemannian geometry$93854199 997 $aUNINA