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v. 1 ISBN 9780444511263
内容説明
The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.
目次
PrefaceList of Contributors1. Solutions of Quasilinear Second-Order Elliptic Boundary Value Problems via Degree Theory (C. Bandle and W. Reichel)2. Stationary Navier-Stokes Problem in a Two-Dimensional Exterior Domain (G.P. Galdi)3. Qualitative Properties of Solutions to Elliptic Problems (W-M. Ni)4. On Some Basic Aspects of the Relationship between the Calculus of Variations and Differential Equations (P. Pedregal)5. On a Class of Singular Perturbation Problems (I. Shafrir)6. Nonlinear Spectral Problems for Degenerate Elliptic Operators (P. Takac)7. Analytical Aspects of Liouville-Type Equations with Singular Sources (G. Tarantello)8. Elliptic Equations Involving Measures (L. Veron)Author IndexSubject Index
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v. 2 ISBN 9780444520456
内容説明
A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.
目次
1. T. Bartsch, Zhi-Qiang Wang, M. Willem: The Dirichlet problem for superlinear elliptic equations.2. B. Dacorogna: Non convex problems of the calculus of variations and differential inclusions.3. Y. Du: Bifurcation and related topics in elliptic problems.4. J. Lopez-Gomez: Metasolutions.5. J. D. Rossi: Elliptic problems with nonlinear boundary conditions and the Sobolev trace theorem.6. G. Rozenblum, M. Melgaard: Schroedinger operators with singular potentials.7. S. Solimini: Multiplicity techniques for problems without compactness.
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v. 3 ISBN 9780444528469
内容説明
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Key features: - Written by well-known experts in the field - Self-contained volume in series covering one of the most rapid developing topics in mathematics
目次
Preface
Contributors
1. S. Antontsev and S. Shmarev: Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions.
2. A. Braides: A Handbook of T-convergence.
3. M. del Pino and M. Musso: Bubbling in nonlinear elliptic problems near criticality.
4. J. Hernandez and F.J. Mancebo: Singular elliptic and parabolic equations.
5. S. Kichenassamy: Schauder-type estimates and applications.
6. A. Lyaghfouri: The Dam problem.
7. L.A. Peletier: Nonlinear eigenvalue problems for higher order model equations.
Index
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v. 4 ISBN 9780444530363
内容説明
A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.
目次
Preface
Contributors
1. F. Brock: Rearrangements and applications to symmetry problems in PDE
2. A. Farina: Liouville-type theorems for elliptic problems
3. M. Guedda: Similarity and pseudosimilarity solutions of degenerate boundary layer equations
4. N. Kenmochi: Monotonicity and compactness methods for nonlinear variational inequalities
5. H. Morimoto: Stationary Navier-Stokes flow in 2-D Channels involving the general outflow condition
6. P. Pucci and J. Serrin: Maximum principles for elliptic partial differential equations
7. V. Radelescu: Singular phenomena in nonlinear elliptic problems from blow-up boundary solutions to equations with singular nonlinearities
Index
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v. 5 ISBN 9780444532176
内容説明
A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.
目次
1. Semilinear elliptic systems: existence, multiplicity, symmetry of solutions (D.G. De Figueiredo)2. Nonlinear variational problems via the fibering method (S. Pohozaev)3. Superlinear elliptic equations and systems (B. Ruf)4. Nonlinear eigenvalue problem with quantization (T. Suzuki and F. Takahashi)5. Stationary problem of Boltzmann equation (S. Ukai and T Yang)6. Existence and stability of spikes for the Gierer-Meinhardt system (J. Wei)
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v. 6 ISBN 9780444532411
内容説明
This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems.
目次
1. Domain Perturbation for Linear and Semi-Linear Boundary Value Problems, D. Daners.
2. Singular solutions of semi-linear elliptic problems J. Davila.
3. Positive solutions to semi- linear and quasi-linear elliptic equations on unbounded domains, V. Kondratiev, V. Liskevich and Z. Sobol.
4. Symmetry of solutions of elliptic equations via maximum principles, F. Pacella and M. Ramaswamy.
5. Stationary Boundary Value Problems for Compressible Navier-Stokes equations, P.I. Plotnikov and J. Sokolowski.
6. Positive Solutions for Lotka-Volterra Systems with Cross- Diffusion, Y. Yamada.
7. Fixed Point Theory and Elliptic Boundary Value Problems, H. Zou.
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