$W^{1,1}_0(Omega)$ in some borderline cases of elliptic equations with degenerate coercivity

We study a degenerate elliptic equation, proving existence results of distributional solutions in some borderline cases.

A semilinear problem with a W^{1,1}_0 solution

We study a degenerate elliptic equation, proving the existence of a W^{1,1}_0 distributional solution.

Existence of solutions for some noncercive elliptic problems involving derivatives of nonlinear terms

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a W^{1,1}_0 solution which is distributional or entropic, according to the growth assumptions on a lower order term in divergence form.

W^{1,1}_0 minima of non coercive functionals

We study an integral non coercive functional defined on H^1_0, proving the existence of a minimum in W^{1,1}_0.

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

We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 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.