Veranstaltungen

12. Dezember 2024, 15:00 bis 17:00

AKOR Seminar: On the regularity of the solution map for polynomials

Seminar

Armin Rainer, VADOR, TU Wien

How do the roots of a monic polynomial whose coefficients depend smoothly on parameters depend on those parameters? This question plays an important role in many areas, e.g., PDEs, perturbation theory of linear operators, and local smooth analysis.   The subject, which started with Rellich’s work in the 1930s, enjoyed sustained interest through time that intensified in the last two decades, bringing some definitive optimal results. In particular, if the coefficients are of class $C^{d-1,1}$, where $d$ is the degree  of the polynomial, then any continuous root is of Sobolev class $W^{1,q}$, for each $1 \le q < d/(d-1)$. In this talk, I will discuss this optimal result and recent work  investigating the continuity of the solution map “coefficients-to-roots”. Joint work with Adam Parusinski

Kalendereintrag

Veranstaltungsort

Sem. R. DB Gelb 04
1040 Wien
Wiedner Hauptstraße 8 E105-4

 

Veranstalter

VADOR
vador@tuwien.ac.at

 

Öffentlich

Nein

 

Kostenpflichtig

Nein

 

Anmeldung erforderlich

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