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We consider nonnegative solutions to $-\Delta u=f(u)$ in half-planes andstrips, under zero Dirichlet boundary condition. Exploiting arotating$\&$sliding line technique, we prove symmetry and monotonicityproperties of the solutions, under very general assumptions on the nonlinearity$f$. In fact we provide a unified approach that works in all the cases$f(0)<0$, $f(0)= 0$ or $f(0)> 0$. Furthermore we make the effort to deal withnonlinearities $f$ that may be not locally-Lipschitz continuous. We alsoprovide explicite examples showing the sharpness of our assumptions on thenonlinear function $f$.

Monotonicity and symmetry of nonnegative solutions to $ -\Delta u=f(u) $ in half-planes and strips