A nonlinear degenerate elliptic problem with W¹,¹₀ solutions

الأصل · EN

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W¹,¹₀ distributional solution under suitable summability assumptions on the source in Lebesgue spaces. Moreover, we prove that our problem has no solution if the source is a Radon measure concentrated on a set of zero harmonic capacity.