also [@chambolle2009homogenization] for a BV approach and [@torres2004plane] for a construction of plane-like solutions with periodic exclusions. Our assumption  implies that the forcing term does not change sign. This restriction has been lifted, under suitable restriction, for periodic media: see [@CLS], which contains an explicit computation in the one-dimensional case; in [@dirr2008pulsating] pulsating waves are constructed under a smallness condition of the forcing term; forced mean curvature motion for graphs, with sign changing velocities, is studied in [@barles2011homogenization] under a rather sharp condition on the forcing term; in that setting, [@cesaroni2013long] explains the construction of generalized traveling waves and analyses the long-time behavior of the motion. When the velocity changes sign, pinning phenomena may occur: this amounts to finding a stationary, positive supersolution at non-vanishing applied load [@dirr2011pinning]. Another very interesting problem is to study the properties of the homogenized motion (the so-called stable norm, or equivalently, the effective Hamiltonian), examining for example its regularity: for periodic coefficients, this question is studied in [@chambolle2014plane].

Notation {#s.notation}
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The symbols $C$ and $c$ denote positive constants which may vary from line to line and, unless otherwise indicated, depend only on the data and on an upper bound for $|p|$ or $\mu$. 