Some elliptic equations with \(W_0^{1,1}\) solutions (Q515921)

The authors are concerned with the regularising effect of some lower order terms in the context of the following quasilinear elliptic problem \[ -\text{div}(|\nabla u|^{p-2}\nabla u)+H(x,u,\nabla u)=f(x)\quad\text{ in }\Omega, \] subject to homogeneous Dirichlet boundary condition. Here \(\Omega\subset {\mathbb R}^N\) \((N\geq 2)\) is a bounded open set and \(1<p\leq N\). The authors investigate how the lower order terms \(f\) and \(H\) can further improve the regularity of \(W_0^{1,1}\) solutions.