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math.AP2025
Weak solutions to Kolmogorov-Fokker-Planck equations: regularity, existence and uniqueness
Pascal Auscher, Cyril Imbert, Lukas Niebel
We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough…
math.AP2025
Fundamental solutions for parabolic equations and systems: universal existence, uniqueness, representation
Pascal Auscher, Khalid Baadi
In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smoot…