Fractional Sobolev Spaces
Universität Heidelberg | Summer 2020
Announcements
NEW DATE: The date of the seminar has changed to Wednesday, 16:00-17:30.
Due to the current situation the course will take place online. Please, register in moodle to keep updated.
The first meeting will take place via video conference on Tuesday, April 21 at 9:15 a.m.
A plan of the topics can be found below, together with the slides of my talks.
Description
Date and place: Tuesday, 9:15-10:45. INF 205 SR2
Abstract: Fractional Sobolev spaces were introduced in the fifties as a generalization of the standard spaces to non-integer orders. They are closely related with the nonlocal partial differential equations, which are attracting a deep interest regarding their applications in a wide range of contexts, including the thin obstacle problem, the fractional Calderón problem, anomalous diffusion and finance.
In this seminar we will study the fractional Sobolev spaces W^{s,p} focusing on the case p=2, when they are Hilbert spaces. We will discuss the equivalence between different definitions, as well as embedding, duality and trace theorems. We will also present some existence and regularity results related with nonlocal equations.
Prerequisites: Previous knowledge on Functional Analysis and Partial Differential Equations would be desirable.
Bibliography:
E. Di Nezza, G. Palatucci, E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136, 521-573, 2012.
W. McLean. Strongly elliptic systems and boundary integral equations, Cambridge University Press, Cambridge, 2000.
Topics
FracSobolev_plan.pdfSlides and notes
Introduction to the seminar
FracSobolev_Intro.pdfAronszajn-Gagliardo-Slobodeckij spaces
FracSobolev_1stDefinition.pdfDiagram with different fractional Sobolev spaces
MAGF_FracSobolevDiagram.pdf