{"product_id":"blowup-theory-for-elliptic-pdes-in-riemannian-geometry-9780691119533","title":"Blowup Theory for Elliptic PDEs in Riemannian","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis work develops critical new ideas and methods for the analysis of elliptic PDEs on compact Riemannian manifolds, especially in the framework of the Yamabe equation, critical Sobolev embedding and blow-up techniques (asymptotic analysis).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This is an important and original work. It develops critical new ideas and methods for the analysis of elliptic PDEs on compact manifolds, especially in the framework of the Yamabe equation, critical Sobolev embedding, and blow-up techniques. This volume will have an important influence on current research.\"\u003cb\u003e—William Beckner, University of Texas at Austin\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  Chapter 1. Background Material 1  1.1 Riemannian Geometry 1  1.2 Basics in Nonlinear Analysis 7  Chapter 2. The Model Equations 13  2.1 Palais-Smale Sequences 14  2.2 Strong Solutions of Minimal Energy 17  2.3 Strong Solutions of High Energies 19  2.4 The Case of the Sphere 23  Chapter 3. Blow-up Theory in Sobolev Spaces 25  3.1 The H 2\/1-Decomposition for Palais-Smale Sequences 26  3.2 Subtracting a Bubble and Nonnegative Solutions 32  3.3 The De Giorgi-Nash-Moser Iterative Scheme for Strong Solutions 45  Chapter 4. Exhaustion and Weak Pointwise Estimates 51  4.1 Weak Pointwise Estimates 52  4.2 Exhaustion of Blow-up Points 54  Chapter 5. Asymptotics When the Energy Is of Minimal Type 67  5.1 Strong Convergence and Blow-up 68  5.2 Sharp Pointwise Estimates 72  Chapter 6. Asymptotics When the Energy Is Arbitrary 83  6.1 A Fundamental Estimate: 1 88  6.2 A Fundamental Estimate: 2 143  6.3 Asymptotic Behavior 182  Appendix A. The Green's Function on Compact Manifolds 201  Appendix B. Coercivity Is a Necessary Condition 209  Bibliography 213","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49526155247959,"sku":"9780691119533","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691119533.jpg?v=1731863160","url":"https:\/\/bookcurl.com\/products\/blowup-theory-for-elliptic-pdes-in-riemannian-geometry-9780691119533","provider":"Book Curl","version":"1.0","type":"link"}