Blow-up Theory for Elliptic PDEs in Riemannian Geometry
Blow-up Theory for Elliptic PDEs in Riemannian Geometry
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DOI：
10.1515/9781400826162
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发表时间：
2004-05
期刊：
影响因子：
--
通讯作者：
Olivier Druet;Emmanuel Hebey;F. Robert
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文献类型：
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作者：
Olivier Druet;Emmanuel Hebey;F. Robert
第1章一夜情背景材料1 1.1黎曼几何1 1.2非线性分析基础7第2章.模型方程13 2.1 Palais-Smale序列14 2.2最小能量的强解17 2.3高能量的强解19 2.4球的情况23第3章.爆破理论在Sobolev空间25 3.1的H 2/1-分解Palais-Smale序列26 3.2减去一个泡沫和非负解32 3.3强解的De Giorgi-Nash-Moser迭代方案45第4章.穷举和弱逐点估计51 4.1弱逐点估计52 4.2爆破点的穷举54第5章。渐近时的能量是最小型67 5.1强收敛和爆破68 5.2夏普逐点估计72第6章.当能量为任意时的渐近性83 6.1基本估计：1 88 6.2基本估计：2 143 6.3渐近行为182附录A。紧流形上的绿色函数201附录B。强制性是必要条件209
Preface 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