Monge-Ampère equations form a pivotal class of fully nonlinear partial differential equations that have deep roots in differential geometry, optimisation and mass transport theories. Their study, ...
Plurisubharmonic functions form a central tool in the study of several complex variables, offering a robust framework for analysing complex phenomena via potential theory. These functions, which are ...
SIAM Journal on Numerical Analysis, Vol. 57, No. 1 (2019), pp. 173-191 (19 pages) In this paper, we establish convergence rate estimates for convex solutions to the Dirichlet problem of the ...
It is well known that the quadratic-cost optimal transportation problem is formally equivalent to the second boundary value problem for the Monge–Ampère equation. Viscosity solutions are a powerful ...