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169 papers · 1 filter
Multiscale analysis of a kinetic equation for mechanotaxis
Benoît Perthame, Francesco Salvarani, Shugo Yasuda
We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for ex…
Notes on Schauder estimates by scaling for elliptic PDEs in divergence form
Stefano Vita
These are the notes of a part of the PhD course Regularity for free boundary problems and for elliptic PDEs, held in Pavia in the spring of 2025. The aim is to provide a comprehens…
Explicit minimisers for anisotropic Riesz energies
Rupert L. Frank, Joan Mateu, Maria Giovanna Mora +3
In this paper we describe explicitly the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisot…
A free boundary approach to the quasistatic evolution of debonding models
Eleonora Maggiorelli, Filippo Riva, Edoardo Giovanni Tolotti
The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existen…
A kinetic theory approach to consensus formation in financial markets
Jean-Gabriel Attali, Francesco Salvarani
It is sometimes acknowledged that (sell-side) equity analysts' recommendations influence investors and therefore market prices. In particular, the S&P 500 is expected to decline (r…
On the hierarchy of plate models for a singularly perturbed multi-well nonlinear elastic energy
Edoardo Giovanni Tolotti
In the celebrated work of Friesecke, James and Müller '06 the authors derive a hierarchy of models for plates by carefully analyzing the -convergence of the rescaled nonlinear e…