Academic Year 2017/2018
- Docente: Antonio Bove
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Moduli: Antonio Bove (Modulo 1) Davide Guidetti (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)
Course contents
Normed spaces; Banach spaces; linear and continuous operators between normed spaces; Baire theorem and applications; Banach-Steinhaus theorem; open mapping theorem and applivations; closed graph theorem; Hahn-Banach theorem and applcations; weak topologies; reflexive Banach spaces; Hilbert spaces; orthogonal projections in Hilbert spaces; Riesz theorem ; Lax-Milgram theorem; compact and self-adjoint operators in Hilbert spaces.
Sobolev spaces; Sobolev embedding theorem; Riesz-Kolmogorov theorem; Rellich-Kondrakov theorem; variational method for the study of elliptic problems; expansions in eigenfunctions; applications to mixed parabolic and hyperbolic problems:
Semigroups and evolution equations; resolvent of a linear operator; Hille-Yosida theorem; applications to mixed parabolic and hyperbolic problems; analytic semigroups; applications to mixed hyperbolic problems.Office hours
See the website of Antonio Bove
See the website of Davide Guidetti