Opuscula Math. 29, no. 4 (2009), 377-391
On elliptic problems with a nonlinearity depending on the gradient
Abstract. We investigate the solvability of the Neumann problem \((1.1)\) involving the nonlinearity depending on the gradient. We prove the existence of a solution when the right hand side \(f\) of the equation belongs to \(L^m(\Omega )\) with \(1 \leq m \lt 2\).
Keywords: Neumann problem, nonlinearity depending on the gradient, \(L^1\) data.
Mathematics Subject Classification: 35D05, 35J25, 35J60.