At the end of the course students should know the basic theory of Sobolev spaces with respect to the Lebesgue measure, of compact operators in normed spaces, and of the variational formulation of elliptic PDEs.
Through exercises solved in the classroom students should understand how to apply his/her theoretic knowledges to solve explicit problems.
Students should be able to evaluate the correctness of the results obtained by himself/herself or by other people.
Students should be able to communicate in a clear and precise way the mathematical contents of the course. Lectures in the classroom and discussion with the teacher will help to be able to use the appropriate scientific language.
Students will be able to deepen their knowledge on the subjects of the course, starting from the basic knowledge given by the course itself. They will be able to consult autonomously specialized monographs, even on related subjects not directly treated in the lectures.