ELEMENTS OF FUNCTIONAL ANALYSIS AND NUMERICAL METHODS ELEMENTI DI ANALISI FUNZIONALE E METODI NUMERICI

A.Y. Credits
2020/2021 9
Lecturer Email Office hours for students
Giovanni Molica Bisci
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

Assigned to the Degree Course

Applied Informatics (LM-18)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location
Date Time Classroom / Location

Program

01 Nonlinear Algebraic Systems:
01.01 Generality and examples;
01.02 A Maximum principle;
01.03 Differential equations;
01.04 Tridiagonal algebraic systems.

02 Algebraic eigenvalues problems:
02.01 Existence of infinite many solutions;
02.02 Direct minimization arguments (Tonelli's result);
02.03 Mountain pass type solutions;
02.04 Multiple solutions.

03 Discrete partial differential equations:
03.01 Generality and examples;
03.02 A Maximum principle;
03.03 Networks and Graphs;
03.04 The Dirichlet problem: infinite many solutions.

04 The discrete p-Laplacian:
04.01 Generality and examples;
04.02 A Maximum principle;
04.03 Spectrum of the discrete linear problem;
04.04 A Direct Minimization result.

05 Anisotropic difference equations:
05.01 Generality and examples;
05.02 Variational formulation;
05.03 Equivalent norms;
05.04 Existence and multiplicity.

06 Dirichlet problem (elliptic case):
06.01 Basic theory on Sobolev Spaces.
06.02 Variational formulation.
06.03 Abstract critical point theorems.
06.04 Existence and multiplicity.

07 Elliptic problems on fractal domains:
07.01 Elements of fractal geometry.
07.02 Sobolev spaces associated to the Sierpinski fractal.
07.03 Embedding results.
07.04 Existence and multiplicity.

08 Elliptic problems on the Euclidean sphere:
08.01 Sobolev spaces on compact varieties.
08.02 Emden-Fowler type equations.
08.03 Stereographic projection and reduction to the sphere.
08.04 Existence and multiplicity.

09 Elliptic problems with lack of compactness
09.01 Generality and examples.
09.02 Symmetries: the Palais principle.
09.03 Schroedinger's equation: existence theorems.
09.04 Elliptic problems on non-compact varieties.

Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Didactics, Attendance, Course Books and Assessment

Course books

H. Brézis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011, xiv+599 pp.

G. Molica Bisci, Variational and Topological Methods for Nonlocal Fractional Periodic Equations, Recent developments in the Nonlocal Theory, De Gruyter, 359-432 (2018).

G. Molica Bisci - V. Radulescu - R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, 162 Cambride University Press - ISBN: 9781107111943. Foreword by J. Mawhin. (pp. 1-400).

S. Salsa, Partial Differential Equations in Action, From Modelling to Theory  - Springer, 2007.

Course books

H. Brézis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011, xiv+599 pp.

G. Molica Bisci, Variational and Topological Methods for Nonlocal Fractional Periodic Equations, Recent developments in the Nonlocal Theory, De Gruyter, 359-432 (2018).

G. Molica Bisci - V. Radulescu - R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia of Mathematics and its Applications, 162 Cambride University Press - ISBN: 9781107111943. Foreword by J. Mawhin. (pp. 1-400).

S. Salsa, Partial Differential Equations in Action, From Modelling to Theory  - Springer, 2007.

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