Elsevier S & T

Handbook of Differential Equations: Stationary Partial Differential Equations: Stationary Partial Differential Equations

Chipot, Michel

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Table of contents
  • Cover
  • Prefacev
  • List of Contributorsvii
  • Contentsix
  • Contents of Volume Ixi
  • Contents of Volume IIxiii
  • Contents of Volume IIIxv
  • Chapter 1. Rearrangements and Applications to Symmetry Problems in PDE1
  • 1. Introduction3
  • 2. Basic definitions6
  • 3. Rearrangements6
  • 4. Inequalities for symmetrizations24
  • 5. Symmetry results37
  • 6. Other symmetry results51
  • List of notations54
  • Acknowledgement55
  • References55
  • Chapter 2. Liouville-Type Theorems for Elliptic Problems61
  • 1. Introduction63
  • 2. Cauchy and Liouville63
  • 3. Hadamard and Liouville65
  • 4. Poisson and Liouville67
  • 5. Bernstein and Liouville75
  • 6. Jörgens and Liouville81
  • 7. De Giorgi and Liouville: Part I83
  • 8. De Giorgi and Liouville: Part II93
  • 9. Harnack and Liouville98
  • 10. Moser and Liouville108
  • Acknowledgements113
  • References113
  • Chapter 3. Similarity and Pseudosimilarity Solutions of Degenerate Boundary Layer Equations117
  • Chapter 3.1. Similarity solutions of degenerate boundary layer equations120
  • 1. Introduction120
  • 2. Similarity reduction122
  • 3. A shooting method and preliminary results128
  • 4. The effects of deceleration of the surface velocity132
  • 5. Global behavior of solutions137
  • 6.Conclusion143
  • Chapter 3.2. Heat transfer in non-Newtonian fluid laminar boundary layer flow along a moving surface144
  • 1. Introduction and laminar boundary layer equations144
  • 2. Main result and ``finite propagation''146
  • 3. Existence of a solution to GB problem and large eta-behavior148
  • 4. Uniqueness results of the GB equation153
  • Chapter 3.3. Exact solution for the heat transfer past a vertical plate with an applied magnetic fie157
  • 1. Introduction157
  • 2. The exact analytic form for negative omega160
  • 3. Blow-up profiles and pseudosimilarity solutions162
  • Chapter 3.4. Mixed convection on a wedge embedded in a porous medium176
  • 1. Introduction176
  • 2. Pseudosimilarity or similarity reductions?179
  • 3. Eigensolutions187
  • 4. Asymptotic solution (epsilon»1)193
  • 5. The limit case beta0 = -194
  • Acknowledgements198
  • References198
  • Chapter 4. Monotonicity and Compactness Methods for Nonlinear Variational Inequalities203
  • 1. Preliminaries205
  • 2. Mappings of monotone type and basic properties215
  • 3. Fixed-point results223
  • 4. Maximal monotonicity of mappings227
  • 5. Perturbations of monotone type234
  • 6. Examples of subdifferentials243
  • 7. Convergence of maximal monotone mappings256
  • 8. Convergence of convex functions265
  • 9. Variational inequalities277
  • 10. Quasi-variational inequalities285
  • References297
  • Chapter 5. Stationary Navier-Stokes Flow in 2-D Channels Involving the General Outflow Condition299
  • 1. Introduction301
  • 2. Function spaces and the symmetry304
  • 3. Channel with one outlet (semi-infinite channel)308
  • 4. Channel with J outlets (J >=2)336
  • 5. Channel contained in T346
  • 6. A characterization of Poiseuille flow350
  • Acknowledgement352
  • References352
  • Chapter 6. Maximum Principles for Elliptic Partial Differential Equations355
  • Section 6.1. Introduction and Preliminaries357
  • 1.1 Introduction357
  • Section 6.2. Tangency and Comparison Theorems for Elliptic Inequalities362
  • 2.1. The contributions of Eberhard Hopf362
  • 2.2. Tangency and comparison principles for quasilinear inequalities368
  • 2.3. Maximum and sweeping principles for quasilinear inequalities371
  • 2.4. Comparison theorems for divergence structure inequalities376
  • 2.5. Tangency theorems via Harnack's inequality379
  • 2.6. Uniqueness of the Dirichlet problem382
  • 2.7. The Boundary Point Lemma383
  • 2.8. Appendix: Proof of Eberhard Hopf's Maximum Principle386
  • Notes390
  • Section 6.3. Maximum Principles for Divergence Structure Elliptic Differential Inequalities391
  • 3.1. Distribution solutions391
  • 3.2. Maximum principles for homogeneous inequalities393
  • 3.3. A maximum principle for thin sets397
  • 3.4. A comparison theorem in W1,p(Omega)399
  • 3.5. Comparison theorems for singular elliptic inequalities401
  • 3.6. Strongly degenerate operators405
  • 3.7. Maximum principles for non-homogeneous elliptic inequalities409
  • 3.8. Uniqueness of the singular Dirichlet problem415
  • 3.9. Maximum principles for structured inequalities416
  • 3.10. Appendix: Sobolev's inequality419
  • Notes420
  • Section 6.4. The Strong Maximum Principle and the Compact Support Principle422
  • 4.1. Introduction422
  • 4.2. A more general inequality424
  • 4.3. Existence theorems425
  • 4.4. The dead core lemma426
  • 4.5. Proof of the Strong Maximum Principle429
  • 4.6. Proof of the Compact Support Principle431
  • 4.7. Strong Maximum Principle: Generalized version432
  • 4.8. Further extensions of the Strong Maximum Principle436
  • Notes438
  • Section 6.5. Applications440
  • 5.1. Cauchy-Liouville theorems440
  • 5.2. Radial symmetry444
  • 5.3. Symmetry for overdetermined boundary value problems451
  • 5.4. The phenomenon of dead cores458
  • 5.5. The Harnack Inequality in R2470
  • 5.6. The Strong Maximum Principle for Riemannian manifolds478
  • Acknowledgement480
  • References480
  • Chapter 7. Singular Phenomena in Nonlinear Elliptic Problems From Blow-Up Boundary Solutions to Equa485
  • 1. Motivation and previous results487
  • 2. Large solutions of elliptic equations with absorption and subquadratic convection term489
  • 3. Singular solutions with lack of the Keller-Osserman condition495
  • 4. Blow-up boundary solutions of the logistic equation503
  • 5. Entire solutions blowing up at infinity of semilinear elliptic systems527
  • 6. Bifurcation problems for singular Lane-Emden-Fowler equations541
  • 7. Sublinear singular elliptic problems with two bifurcation parameters552
  • 8. Bifurcation and asymptotics for the singular Lane-Emden-Fowler equation with a convection term564
  • References590
  • Author Index595
  • Subject Index603
Book details
  • Vendor Elsevier S & T
  • SKU 9780444530363
  • ISBN-13 9780080521831
  • Author Chipot, Michel
  • Category Mathematics
  • Subject Mathematical Analysis

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