Author | Chipot, Michel. author |
---|---|
Title | Elements of Nonlinear Analysis [electronic resource] / by Michel Chipot |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8428-0 |
Descript | VII, 256 p. online resource |
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