  In this work we analyze regularized optimal transport problems in the
so-called Kantorovich form, i.e. given two Radon measures on two compact sets,
the aim is to find a transport plan, which is another Radon measure on the
product of the sets, that has these two measures as marginals and minimizes the
sum of a certain linear cost function and a regularization term. We focus on
regularization terms where a Young's function applied to the (density of the)
transport plan is integrated against a product measure. This forces the
transport plan to belong to a certain Orlicz space. The predual problem is
derived and proofs for strong duality and existence of primal solutions of the
regularized problem are presented. Existence of (pre-)dual solutions is shown
for the special case of $L^p$ regularization for $p\geq 2$. Moreover, two
results regarding $\Gamma$-convergence are stated: The first is concerned with
marginals that do not lie in the appropriate Orlicz space and guarantees
$\Gamma$-convergence to the original Kantorovich problem, when smoothing the
marginals. The second results gives convergence of a regularized and
discretized problem to the unregularized, continuous problem.
