The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.
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A nonconforming virtual element method is developed for the vanishing moment approximation of the Monge-Ampère equation in 2D, with optimal a priori error estimates in H2, H1 and L2 norms plus existence and uniqueness of the discrete solution.
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An Affine Invariant Minkowski Problem
The paper solves the affine-invariant Minkowski problem for convex domains invariant under specific discrete affine subgroups by establishing a local Steiner formula and applying a variational method based on covolume convexity.
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Nonconforming virtual element method for the Monge-Amp\`ere equation
A nonconforming virtual element method is developed for the vanishing moment approximation of the Monge-Ampère equation in 2D, with optimal a priori error estimates in H2, H1 and L2 norms plus existence and uniqueness of the discrete solution.