Il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terrà lunedì 17 febbraio 2025 alle ore 15.00, nella Sala Riunioni Primo Livello (SR1). Di seguito titoli e abstract.

Antonia Diana: 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 R^2, which evolves by the L^2-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=+∞.

Domenico Vuono: Second and third order estimates for solutions to $p$-Laplace equations.