The -membranes problem for quasilinear degenerate systems

  • José Francisco Rodrigues

    FC Universidade de Lisboa, Portugal
  • Lisa Santos

    Universidade do Minho, Braga, Portugal
  • Assis Azevedo

    Universidade Do Minho, Braga, Portugal


We study the regularity of the solution of the variational inequality for the problem of -membranes in equilibrium with a degenerate operator of -Laplacian type, , for which we obtain the corresponding Lewy–Stampacchia inequalities. By considering the problem as a system coupled through the characteristic functions of the sets where at least two membranes are in contact, we analyze the stability of the coincidence sets.

Cite this article

José Francisco Rodrigues, Lisa Santos, Assis Azevedo, The -membranes problem for quasilinear degenerate systems. Interfaces Free Bound. 7 (2005), no. 3, pp. 319–337

DOI 10.4171/IFB/127