Annali di Matematica Pura ed Applicata

, Volume 148, Issue 1, pp 117–130 | Cite as

Asymptotic spherical symmetry of the free boundary in degenerate diffusion equations

  • Martino Bardi


A general class of nonlinear degenerate parabolic equations in many space dimensions is considered and two main results concerning the free boundary are proved: (i) the «eventual» Lipschitz continuity in the space variable, (ii) the asymptotic spherical symmetry in a stronger sense than the «almost radiality» proved by Aronson & Caffarelli [2] for the porous medium equation. The proofs make use of geometric ideas based on the comparison principle and the method of moving planes.


Porous Medium Parabolic Equation Free Boundary General Class Space Dimension 
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© Fondazione Annali di Matematica Pura ed Aplicata 1987

Authors and Affiliations

  • Martino Bardi
    • 1
  1. 1.Seminario MatematicoUniversità di PadovaPadovaItaly

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