On certain anisotropic elliptic equations arising in congested optimal transport: local gradient bounds

@inproceedings{Brasco2014OnCA,
  title={On certain anisotropic elliptic equations arising in congested optimal transport: local gradient bounds},
  author={Lorenzo Brasco and Guillaume Carlier},
  year={2014}
}
Motivated by applications to congested optimal transport problems, we prove higher integrability results for the gradient of solutions to some anisotropic elliptic equations, exhibiting a wide range of degeneracy. The model case we have in mind is the following: ∂x [ (|ux| − δ1) q−1 + ux |ux| ] 

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