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Explicit and uniform estimates for second order divergence operators on LP spaces
03 Dec
03. December 2019
Oberseminar Analysis und Theoretische Physik

Explicit and uniform estimates for second order divergence operators on LP spaces

It is the aim of the talk to give – aside the Beurling/Deny approach – a consistent definition of second order divergence operators on spaces, even if the underlying domain is highly non-smooth, the boundary conditions are mixed and the coefficient function is real, bounded and elliptic – but not necessarily symmetric. In order to do this, one first proves that, under minimal assumptions, the resolvent transports the spaces with sufficiently large into. This shows that, for these, the part of the operator in possesses a domain which embeds into. Having this at hand, one can modify ideas of Cialdea/Maz’ya to include the numerical range in a certain sector. This leads to suitable resolvent estimates. Moreover, we prove that the resulting semigroup is contractive and analytic with explicitly determined holomorphy angle. Finally, a holomorphic calculus is established with (half) angle smaller than. This gives even maximal parabolic regularity via the Dore/Venni theorem.

Speaker

Dr. Joachim Rehberg (WIAS Berlin)

Organiser

Institut für Angewandte Mathematik
Welfengarten 1
30167 Hannover

Date

03. December 2019
15:00 o'clock - 17:00 o'clock

Public contact

Antje Günther
Institut für Angewandte Mathematik
Welfengarten 1
30167 Hannover
Tel.: 0511/762-3251
Fax: 0511/762-3988
guenther@ifam.uni-hannover.de

Location

Leibniz Universität Hannover
Building: 1101
Room: C311
Welfengarten 1
30167 Hannover
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