Dear all,

Here is the announcement of the next MAP seminar.

⟶ Thursday 5 December, at 11:30 in Aula Seminari and online on Google Meet: https://meet.google.com/vtt-bhkm-tzc.

⟶ *Speaker**:* *Antonia Diana* (Sapienza Università di Roma)

⟶ *Title**:* *Length–penalized elastic flow of curves with partial free boundary*

⟶ *Abstract**:* Geometric gradient flows for elastic energies play an important role in mathematics and in many applications. In this talk we consider a curve with boundary points free to move on a line in ℝ2, which evolves by the L2-gradient flow of the *elastic energy*, that is a linear combination of the Willmore and the length functional. For such planar evolution problem we study the short and long–time existence. Once we establish the well–posedness in the case of “*Navier*” boundary conditions, employing the Solonnikov theory for linear parabolic systems in Hölder space, we show that there exists a unique flow in a maximal time interval [0,T) and it is unique in a purely geometric sense. Finally, using energy methods we prove that maximal time is actually T=∞.

We remind you that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

See you soon,

The organizers: Michele Caselli Francesco Malizia Jeremy Mirmina Filippo Paiano Leonardo Roveri

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