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math.AP2025
Semi-discrete optimal transport techniques for the compressible semi-geostrophic equations
David P. Bourne, Charlie P. Egan, Théo Lavier +1
We prove existence of weak solutions of the 3D compressible semi-geostrophic (SG) equations with compactly supported measure-valued initial data. These equations model large-scale…
math.AP2020
Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators
Usman Hafeez, Théo Lavier, Lucas Williams +1
We investigate a connection between solvability of the Dirichlet problem for an infinitely degenerate elliptic operator and the validity of an Orlicz-Sobolev inequality in the asso…