Travelling graphs for the forced mean curvature motion in an arbitrary space dimension
Résumé
We construct travelling wave graphs of the form z = -ct phi(x), phi : x is an element of RN-1 -> phi(x) is an element of R, N >= 2, solutions to the N-dimensional forced mean curvature motion V-n = -co + k (c >= co) with prescribed asymptotics. For any 1-homogeneous function phi(infinity) , viscosity solution to the eikonal equation vertical bar D phi(infinity)vertical bar =root(c/c0)(2) - 1, we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by phi(infinity). We also describe phi(infinity) in terms of a probability measure on SN-2.
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