3 papers
math.AP2026
The fundamental solution of a nonlinear kinetic Fokker-Planck equation
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has i…
math.AP2025
Introduction to quantitative De Giorgi methods
Giovanni Brigati, Clément Mouhot
The theory of De Giorgi (1958) and Nash (1959) solves Hilbert's 19th problem and constitutes a major advance in the analysis of PDEs in the 20th century. This theory concerns the H…
math.FA2025
Non-bilinear Dirichlet Functionals: Markovianity, locality, invariance
Giovanni Brigati, Lorenzo Dello Schiavo
We present in a unified setting the foundations for a theory of non-bilinear Dirichlet functionals on Hilbert spaces. We prove known and new equivalences between non-linear semigro…