Elements of nonlinear analysis
著者
書誌事項
Elements of nonlinear analysis
（Birkhäuser advanced texts : Basler Lehrbücher / edited by Herbert Amann, Hanspeter Kraft）
Birkhäuser Verlag, c2000
大学図書館所蔵 件 / 全27件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. [251]-254) and index
内容説明・目次
内容説明
"This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --MATHEMATICAL REVIEWS
目次
1. Some Physical Motivations.- 1.1. An elementary theory of elasticity.- 1.2. A problem in biology.- 1.3. Exercises.- 2. A Short Background in Functional Analysis.- 2.1. An introduction to distributions.- 2.2. Integration on boundaries.- 2.3. Introduction to Sobolev spaces.- 2.4. Exercises.- 3. Elliptic Linear Problems.- 3.1. The Dirichlet problem.- 3.2. The Lax-Milgram theorem and its applications.- 3.3. Exercises.- 4. Elliptic Variational Inequalities.- 4.1. A generalization of the Lax-Milgram theorem.- 4.2. Some applications.- 4.3. Exercises.- 5. Nonlinear Elliptic Problems.- 5.1. A compactness method.- 5.2. A monotonicity method.- 5.3. A generalization of variational inequalities.- 5.4. Some multivalued problems.- 5.5. Exercises.- 6. A Regularity Theory for Nonlocal Variational Inequalities.- 6.1. Some general results.- 6.2. Applications to second order variational inequalities.- 6.3. Exercises.- 7. Uniqueness and Nonuniqueness Issues.- 7.1. Uniqueness result for local nonlinear problems.- 7.2. Nonuniqueness issues.- 7.3. Exercises.- 8. Finite Element Methods for Elliptic Problems.- 8.1. An abstract setting.- 8.2. Some simple finite elements.- 8.3. Interpolation error.- 8.4. Convergence results.- 8.5. Approximation of nonlinear problems.- 8.6. Exercises.- 9. Minimizers.- 9.1. Introduction.- 9.2. The direct method.- 9.3. Applications.- 9.4. The Euler Equation.- 9.5. Exercises.- 10. Minimizing Sequences.- 10.1. Some model problems.- 10.2. Young measures.- 10.3. Construction of the minimizing sequences.- 10.4. A more elaborate issue.- 10.5. Numerical analysis of oscillations.- 10.6. Exercises.- 11. Linear Parabolic Equations.- 11.1. Introduction.- 11.2. Functional analysis for parabolic problems.- 11.3. The resolution of parabolic problems.- 11.4. Applications.- 11.5. Exercises.- 12. Nonlinear Parabolic Problems.- 12.1. Local problems.- 12.2. Nonlocal problems.- 12.3. Exercises.- 13. Asymptotic Analysis.- 13.1. The case of one stationary point.- 13.2. The case of several stationary points.- 13.3. A nonlinear case.- 13.4. Blow-up.- 13.5. Exercises.
「Nielsen BookData」 より
