Partial Differential Equations
A.Y. 2018/2019
Learning objectives
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
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
Second semester
Course syllabus
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.
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.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Lessons: 42 hours
Professor:
Ruf Bernhard