Luca ESPOSITO | HIGHER ANALYSIS
Luca ESPOSITO HIGHER ANALYSIS
cod. 0522200004
HIGHER ANALYSIS
| 0522200004 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF7 | |
| MATHEMATICS | |
| 2019/2020 |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| PRIMO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| THE TEACHING PROVIDES ADVANCED KNOWLEDGE AND METHODS OF MATHEMATICAL ANALYSIS OF COMMON USE IN MODERN ANALYSIS AWARENESS: KNOW THE MAIN TOPICS ABOUT SOBOLEV SPACES. THE COURSE WILL BRING THE STUDENT TO USE WEAK FORMULATION OF SOME EASY BOUNDARY VALUE PROBLEM. COMUNICATIVE ABILITIES: THE STUDENT WILL BE ABLE TO ARTICULATE THE STATEMENTS AND THE PROOF OF THE THEOREM DEALED IN THE COURSE. EDUCATIONAL SKILLS: THE STUDENT WILL ACQUIRE THE KNOWLEDGE OF MATEMATICAL TOOLS THAT ALLOW HIM TO HANDLE WITH MORE ADVANCED MATEMATOCAL TOPICS. |
| Prerequisites | |
|---|---|
| KNOWLEDGE OF THE THEORY OF FUNCTIONS OF SEVERAL VARIABLES. MEASURE AND RIEMANN INTEGRALS IN R^N. BASIC TOPOLOGY. |
| Contents | |
|---|---|
| 1. SOBOLEV SPACES IN DIMENSION 1. 2. SOME EXAMPLES OF BOUNDARY VALUE PROBLEM. 3. THE MAXIMUM PRINCIPLE. 4. DEFINITIONS AND ELEMENTARY PROPERTIES OF THE SOBOLEV SPACES IN DIMENSION N. 5. EXTENSION OPERATORS. 6. SOBOLEV INEQUALITIES. 7. VARIATIONAL FORMULATION OF SOME BOUNDARY VALUE PROBLEM. 8. REGULARITY OF WEAK SOLUTIONS. |
| Teaching Methods | |
|---|---|
| FRONTAL LESSONS |
| Verification of learning | |
|---|---|
| THE STUDENT WILL TAKE AN ORAL EXAMINATION CONCERNING THE TOPICS COVERED IN THE COURSE. |
| Texts | |
|---|---|
| H. BREZIS, ANALISI FUNZIONALE, LIGUORI EDITORE. L.C. EVANS R.F. GARIEPY MEASURE THEORY AND FINE PROPERTIES OF FUNCTIONS |
| More Information | |
|---|---|
| WEB: HTTP://WWW.DIPMAT2.UNISA.IT/PEOPLE/ESPOSITO/WWW/AMIIIMAT.HTML |
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