First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
MATHEMATICS
Course unit
FUNCTIONS THEORY
SCP3050963, A.A. 2015/16

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course Second cycle degree in
MATHEMATICS
SC1172, Degree course structure A.Y. 2011/12, A.Y. 2015/16
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Degree course track GENERALE [010PD]
Number of ECTS credits allocated 8.0
Type of assessment Mark
Course unit English denomination FUNCTIONS THEORY
Website of the academic structure http://matematica.scienze.unipd.it/2015/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English
Branch PADOVA
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Lecturers
Teacher in charge PIER DOMENICO LAMBERTI MAT/05

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses MAT/05 Mathematical Analysis 8.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
hours
Hours of
Individual study
Shifts
Practice 4.0 32 68.0 No turn
Lecture 4.0 32 68.0 No turn

Calendar
Start of activities 01/03/2016
End of activities 15/06/2016
Show course schedule 2019/20 Reg.2011 course timetable

Examination board
Board From To Members of the board
6 Teoria delle Funzioni - a.a. 2018/2019 01/10/2018 30/09/2019 VITTONE DAVIDE (Presidente)
MARTINAZZI LUCA MASSIMO ANDREA (Membro Effettivo)
CIATTI PAOLO (Supplente)
MARICONDA CARLO (Supplente)
MONTI ROBERTO (Supplente)
5 Teoria delle Funzioni - 2017/2018 01/10/2017 30/09/2018 LANZA DE CRISTOFORIS MASSIMO (Presidente)
LAMBERTI PIER DOMENICO (Membro Effettivo)
CIATTI PAOLO (Supplente)
MARICONDA CARLO (Supplente)
MONTI ROBERTO (Supplente)
4 Teoria delle Funzioni - 2016/2017 01/10/2016 30/11/2017 LAMBERTI PIER DOMENICO (Presidente)
LANZA DE CRISTOFORIS MASSIMO (Membro Effettivo)
CIATTI PAOLO (Supplente)
MARICONDA CARLO (Supplente)
MONTI ROBERTO (Supplente)
3 Teoria delle Funzioni - a.a. 2015/2016 01/10/2015 30/11/2016 LAMBERTI PIER DOMENICO (Presidente)
MONTI ROBERTO (Membro Effettivo)
CIATTI PAOLO (Supplente)
GUIOTTO PAOLO (Supplente)
MARICONDA CARLO (Supplente)

Syllabus
Prerequisites: Measure Theory and Lebesgue integration: basic definitions, classical theorems for passing to the limit under integral sign, Tonelli and Fubini Theorems, basic notions on L^p spaces.
Target skills and knowledge: Notion of weak derivative and definition of Sobolev space on a domain in the n-dimensional euclidean space. Main theorems of the Theory of Sobolev Spaces: approximation, integral representation, embedding, extension, trace theorems. Applications of the theory of Sobolev spaces: weak formulation of a boundary value problem for a partial differential equation and existence of solutions by means of the variational approach.

Ability to apply integral inequalities in order to analyze and compare integral norms of functions and their derivatives, ability to deal with approximation procedures in function space, ability to set up a differential problem in the weak form.
Examination methods: Written and oral examination
Assessment criteria: In order to obtain a final grade between 18 and 23 it is necessary to know all statements of all definitions, theorems, lemmas, corollaries, the main examples and counterexamples, and to be able to solve standard exercises. For grades above 23 it is necessary to know also all the proofs of all propositions, and to be able to solve less repetitive exercises.
Course unit contents: Theory of Sobolev spaces and applications. Preliminaries on L_p spaces. Weak derivatives. Standard Sobolev spaces and their variants. Lipschitz continuous functions and the Rademacher Theorem. Approximation theorems. Integral representations. Embedding theorems. Estimates for intermediate derivatives. Compact embeddings. Besov-Nikolskii spaces. Trace theorems. Extension theorems. Applications: existence of solutions to the Poisson and Dirichlet problems, and to the Helmholtz equation.
Planned learning activities and teaching methods: Traditional lectures.
Textbooks (and optional supplementary readings)
  • Victor I. Burenkov, Sobolev Spaces on domains. Stuttgart: B. G. Teubner Verlagsgesellschaft mbH, 1998. Cerca nel catalogo