The course presents the basic concepts of the modern theory of Partial Differential Equations.
Expected learning outcomes
Acquisition of the basic notions and the techniques for solving partial differential equations. Study of the relations with the theory of function spaces, and of various fundamental properties such as maximum principle, weak solutions and regularity theory.
Lesson period: Second semester
(In case of multiple editions, please check the period, as it may vary)
Representaion formulas for solutions, fundamental solution, Green's function, Sobolev spaces, weak derivatives, Sobolev inequalities and embeddings, compactness and the theorem of Rellich Kondrachov, linear elliptic equations of second order, existence and uniqueness of weak solutions for the Dirichlet problem, regularity of weak solutions, maximum principle, lemma of Hopf, ortonormal basis of eigenfunctions, variational characterization of eigenvalues.