Partial differential equations 2

1. Sobolev spaces. Lax-Milgram Theorem.
2. Elliptic linear BVPs, weak solutions, existence and uniqueness.
3. Eigenvalues of symmetric elliptic operators.
4. Parabolic linear Cauchy problem, solution of the heat equation.
5. Weak solution of parabolic linear IBVPs: Galerkin method and energy estimates.
6. Elliptic nonlinear BVPs, weak solutions,
7. Uniformly monotone and Lipschitz continuous operators. Solvability theorem for the elliptic BVP.