Care tutte, cari tutti,
La settimana prossima avremo due eventi per il ciclo dei Seminari di Analisi:
• Mercoledì 9 ottobre, ore 17, avremo il piacere di ascoltare Alex Kaltenbach (TUB), che terrà un seminario dal titolo “A finite element approximation of a simplified model for smart fluids: an error analysis"
• Giovedì 10 ottobre, ore 17, avremo il piacere di ascoltare David Bate (Warwick), che terrà un seminario dal titolo “Alberti representations, rectifiability and regularity of measures satisfying a PDE”.
Trovate sotto gli abstract.
Ricordiamo anche che oggi alle 17 in Aula Riunioni ci sarà il seminario di Chiara Boccato (UniPi), preceduto da uno snack nella stessa aula alle 16:45.
A presto,
Ilaria Lucardesi e Luigi Forcella
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Dear all,
The next week we will have two events for the Mathematical Analysis Seminars:
• Wednesday 9 October, 5PM, we will have the pleasure of listening to Alex Kaltenbach (TUB).The title of the talk is “A finite element approximation of a simplified model for smart fluids: an error analysis”.
• Thursday 10 October, 5PM, we will have the pleasure of listening to David Bate (Warwick).The title of the talk is “Alberti representations, rectifiability and regularity of measures satisfying a PDE”.
Below the abstracts.
We remind that today at 5PM there will be the seminar by Chiara Boccato (UniPi) in Aula Riunioni, with a snack in the same room at 4:45 pm.
Best regards,
Ilaria Lucardesi and Luigi Forcella.
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Speaker: Alex Kaltenbach
Title: A finite element approximation of a simplified model for smart fluids: an error analysis
Abstract: In this talk, a finite element approximation of the steady p(⋅)p(⋅)-Navier-Stokes equations (p(⋅)p(⋅) is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the apriori error estimates (for the velocity).
The steady p(⋅)p(⋅)-Navier-Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called smart fluids,e.g., electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, e.g., in electronic, automobile, heavy machinery, military, and biomedical industry.
Speaker: David Bate.
Title: Alberti representations, rectifiability and regularity of measures satisfying a PDE
Abstract: An Alberti representation of a (finite, Borel) measure is a decomposition into 1-rectifiable measures. By Fubini's theorem, Lebesgue measure on [0,1]^n has n "independent" Alberti representations, each one consisting of curves parallel to a coordinate axis. This naturally extends to representations of n-rectifiable sets in Euclidean space, where the tangents to curves span the approximate tangent space almost everywhere, and can be extended further to rectifiable subsets of a metric space. This talk will consider the converse statement. We will show that, if n-dimensional Hausdorff measure of a metric space X has n independent Alberti representations, then X is n-rectifiable. This result has numerous applications to rectifiability in metric spaces that will be discussed. We will also discuss a key element of the proof on the integrability of measuressatisfying a PDE constraint. This talk is based on joint work with Tuomas Orponen and Julian Weigt.
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Luigi Forcella, Assistant Professor (RTD-B, tenure-track)
University of Pisa
Department of Mathematics
Largo Bruno Pontecorvo 5
57127 Pisa, Italy
https://pagine.dm.unipi.it/forcella/index.html
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Luigi Forcella, Assistant Professor (RTD-B, tenure-track)
University of Pisa
Department of Mathematics
Largo Bruno Pontecorvo 5
57127 Pisa, Italy
https://pagine.dm.unipi.it/forcella/index.html
