## Alessandro Carlotto: Catalogue data in Spring Semester 2018 |

Name | Dr. Alessandro Carlotto |

Field | Mathematics |

Department | Mathematics |

Relationship | Assistant Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3462-00L | Functional Analysis II | 10 credits | 4V + 1U | A. Carlotto | |

Abstract | Fundamentals of the theory of distributions, Sobolev spaces, weak solutions of elliptic boundary value problems (solvability results both via linear methods and via direct variational methods), elliptic regularity theory, Schauder estimates, selected applications coming from physics and differential geometry. | ||||

Learning objective | Acquiring the language and methods of the theory of distributions in order to study differential operators and their fundamental solutions; mastering the notion of weak solutions of elliptic problems both for scalar and vector-valued maps, proving existence of weak solutions in various contexts and under various classes of assumptions; learning the basic tools and ideas of elliptic regularity theory and gaining the ability to apply these methods in important instances of contemporary mathematics. | ||||

Lecture notes | Lecture notes "Funktionalanalysis II" by Michael Struwe. | ||||

Literature | Useful references for the course are the following textbooks: Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. David Gilbarg, Neil Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin, 2001. Qing Han, Fanghua Lin. Elliptic partial differential equations. Second edition. Courant Lecture Notes in Mathematics, 1. Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2011. Michael Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011. Lars Hörmander. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis. Classics in Mathematics. Springer-Verlag, Berlin, 2003. | ||||

Prerequisites / Notice | Functional Analysis I plus a solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces). | ||||

401-5350-00L | Analysis Seminar | 0 credits | 1K | M. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, T. Kappeler, T. Rivière, D. A. Salamon | |

Abstract | Research colloquium | ||||

Learning objective | |||||

Content | Research seminar in Analysis | ||||

406-3461-AAL | Functional Analysis I Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 10 credits | 21R | A. Carlotto | |

Abstract | Baire category; Banach spaces and linear operators; Fundamental theorems: Open Mapping Theorem, Closed Range Theorem, Uniform Boundedness Principle, Hahn-Banach Theorem; Convexity; reflexive spaces; Spectral theory. | ||||

Learning objective | |||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |