Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal transport approach to Sobolev regularity of solutions to the
  weighted least gradient problem   We study the equivalence between the weighted least gradient problem and the
weighted Beckmann minimal flow problem or equivalently, the optimal transport
problem with Riemannian cost. Thanks to this equivalence, we prove existence
and uniqueness of a solution to the weighted least gradient problem. Then, we
show $L^p$ regularity on the transport density between two singular measures in
the corresponding equivalent Riemannian optimal transport formulation. This
will imply $W^{1,p}$ regularity of the solution of the weighted least gradient
problem.

22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
1
The categories of this paper are: cs
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics