  Let X be a smooth projective variety over a complete discretely valued field
of mixed characteristic. We solve non-archimedean Monge-Amp\`ere equations on X
assuming resolution and embedded resolution of singularities. We follow the
variational approach of Boucksom, Favre, and Jonsson proving the continuity of
the plurisubharmonic envelope of a continuous metric on an ample line bundle on
X. We replace the use of multiplier ideals in equicharacteristic zero by the
use of perturbation friendly test ideals introduced by Bhatt, Ma, Patakfalvi,
Schwede, Tucker, Waldron, and Witaszek building upon previous constructions by
Hacon, Lamarche, and Schwede.
