Partial differential equations 2 (János Karátson, 2019)
- Sobolev spaces. Lax-Milgram Theorem.
- Elliptic linear BVPs, weak solutions, existence and uniqueness.
- Eigenvalues of symmetric elliptic operators.
- Parabolic linear Cauchy problem, solution of the heat equation.
- Weak solution of parabolic linear IBVPs: Galerkin method and energy estimates.
- Elliptic nonlinear BVPs, weak solutions,
- Uniformly monotone and Lipschitz continuous operators. Solvability theorem for the elliptic BVP.