Author | Chipot, Michel. author |
---|---|
Title | โ Goes to Plus Infinity [electronic resource] / by Michel Chipot |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8173-9 |
Descript | VIII, 181 p. online resource |
1. Introduction to Linear Elliptic Problems -- 1.1. The LaxโMilgram theorem -- 1.2. Elementary notions on Sobolev spaces -- 1.3. Applications to linear elliptic problems -- 2. Some Model Techniques -- 2.1. The case of lateral Dirichlet boundary conditions on a rectangle -- 2.2. The case of lateral Neumann boundary conditions on a rectangle -- 2.3. The case of lateral Dirichlet boundary conditions revisited -- 2.4. A different point of view -- 3. A General Asymptotic Theory for Linear Elliptic Problems -- 3.1. A general convergence result in H1 (S24,) -- 3.2. A sharper rate of convergence -- 3.3. Convergence in higher Sobolev spaces -- 4. Nonlinear Elliptic Problems -- 4.1. Variational inequalities -- 4.2. Quasilinear elliptic problems -- 4.3. Strongly nonlinear problems -- 5. Asymptotic Behaviour of some Nonlinear Elliptic Problems -- 5.1. The case of variational inequalities -- 5.2. The case of quasilinear problems -- 6. Elliptic Systems -- 6.1. Some inequalities -- 6.2. Existence results for linear elliptic systems -- 6.3. Nonlinear elliptic systems -- 7. Asymptotic Behaviour of Elliptic Systems -- 7.1. The case of linear elliptic systems satisfying the Legendre condition -- 7.2. The system of elasticity -- 8. Parabolic Equations -- 8.1. Functional spaces for parabolic problems -- 8.2. Linear parabolic problems -- 8.3. Nonlinear parabolic problems -- 9. Asymptotic Behaviour of Parabolic Problems -- 9.1. The linear case -- 9.2. A nonlinear case -- Concluding Remark