04995nam 22010694a 450 991077809780332120200520144314.01-282-08723-11-282-93537-2978661293537497866120872331-4008-2616-010.1515/9781400826162(CKB)1000000000756335(EBL)445417(OCoLC)367689143(SSID)ssj0000113336(PQKBManifestationID)11145499(PQKBTitleCode)TC0000113336(PQKBWorkID)10101454(PQKB)10728495(DE-B1597)446346(OCoLC)979578332(DE-B1597)9781400826162(Au-PeEL)EBL445417(CaPaEBR)ebr10284256(CaONFJC)MIL293537(MiAaPQ)EBC445417(PPN)17026968X(EXLCZ)99100000000075633520031117d2004 uy 0engurcn|||||||||txtccrBlow-up theory for elliptic PDEs in Riemannian geometry[electronic resource] /Olivier Druet, Emmanuel Hebey, Frédéric RobertCourse BookPrinceton, N.J. Princeton University Pressc20041 online resource (227 p.)Mathematical Notes ;45Description based upon print version of record.0-691-11953-8 Includes bibliographical references (p. [213]-218).Front matter --Contents --Preface --Chapter 1. Background Material --Chapter 2. The Model Equations --Chapter 3. Blow-up Theory in Sobolev Spaces --Chapter 4. Exhaustion and Weak Pointwise Estimates --Chapter 5. Asymptotics When the Energy Is of Minimal Type --Chapter 6. Asymptotics When the Energy Is Arbitrary --Appendix A. The Green's Function on Compact Manifolds --Appendix B. Coercivity Is a Necessary Condition --BibliographyElliptic 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.Mathematical NotesCalculus of variationsDifferential equations, NonlinearGeometry, RiemannianAsymptotic analysis.Cayley–Hamilton theorem.Contradiction.Curvature.Diffeomorphism.Differentiable manifold.Equation.Estimation.Euclidean space.Laplace's equation.Maximum principle.Nonlinear system.Polynomial.Princeton University Press.Result.Ricci curvature.Riemannian geometry.Riemannian manifold.Simply connected space.Sphere theorem (3-manifolds).Stone's theorem.Submanifold.Subsequence.Theorem.Three-dimensional space (mathematics).Topology.Unit sphere.Calculus of variations.Differential equations, Nonlinear.Geometry, Riemannian.515/.35331.45bclDruet Olivier1976-1542996Hebey Emmanuel1964-61069Robert Frédéric1974-1576416MiAaPQMiAaPQMiAaPQBOOK9910778097803321Blow-up theory for elliptic PDEs in Riemannian geometry3854199UNINA