Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle

Abstract

In this work, we study surfaces over convex regions in ℝ2 which are evolving by the mean curvature flow. Here, we specify the angle of contact of the surface to the boundary cylinder. We prove that solutions converge to ones moving only by translation.

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Partially supported by the NSF grant no: DMS-9100383

Partially supported by the NSF grant no: DMS 9108269.A01

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Altschuler, S.J., Wu, L.F. Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle. Calc. Var 2, 101–111 (1994). https://doi.org/10.1007/BF01234317

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Mathematics subject classification

  • 35K20
  • 58G11