JournalsjemsVol. 7, No. 3pp. 319–359

Mean curvature properties for p-Laplace phase transitions

  • Berardino Sciunzi

    Università della Calabria, Arcavacata di Rende, Italy
  • Enrico Valdinoci

    Università di Roma Tor Vergata, Italy
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Abstract

This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of pp-Laplacian type and a double well potential h0h_0 with suitable growth conditions. We prove that level sets of solutions of Δpu=h0(u)\Delta_p u=h_0'(u) possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.

Cite this article

Berardino Sciunzi, Enrico Valdinoci, Mean curvature properties for p-Laplace phase transitions. J. Eur. Math. Soc. 7 (2005), no. 3, pp. 319–359

DOI 10.4171/JEMS/31