Chap1: ODE Methods
1.1. The case of the line
1.2. The case of the interval
1.3. The case of Rn, n greater than 2
1.4. The case of the ball of Rn, n greater than 2
Chap2: Variational Methods
2.1. Linear elliptic equations
2.2. C1 funtionals
2.3. Global Minimization
2.4. Constrained minimizations
2.5. The mountain pass theorem
2.6. Specific methods in Rn
2.7. Study of a model case
Chap3: Methods of super and subsolutions
3.1. The maximum principles
3.2. The spectral decomposition of the Laplacian
3.3. The iteration method
3.4. The equation -laplacian of u= lambda times g(u)
Chap4: Regularity and qualitative properties
4.1. Interior regularity for linear equations
4.2. Lp regularity for linear equations
4.3. Co regularity for linear equations
4.4. Bootstrap methods
4.5. Symmetry of positive solutions
Chap5: Appendix: Sobolev Spaces
5.1. Definitions and basic properties
5.2. Sobolev spaces and Fourier transform
5.3. The chain rule and applications
5.4. Sobolev's inequalities
5.5. Compactness properties
5.6. Compactness properties in Rn
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