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We study a nonlinear equation with an elliptic operator having degeneratecoercivity. We prove the existence of a unique W^{1,1}_0 distributionalsolution under suitable summability assumptions on the source in Lebesguespaces. Moreover, we prove that our problem has no solution if the source is aRadon measure concentrated on a set of zero harmonic capacity.

A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions