A Parabolic Equation with a Mean-Curvature Type Operator

  • Michiel Bertsch
  • Roberta Dal Passo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)


The classical mean-curvature operator arises in geometry, and is given by. Mathematically this operator is of particular interest because of its degeneracy for large gradients. The same type of operators arises also in thermodynamical context in the theory of convex free energy functionals, which are asymptotically linear as the gradient tends to infinity [12]; in particular this leads to the parabolic equation u t = Lu [6]. Observe that here u is supposed to be a function, i.e. u is single-valued, in contrast to the geometric origin of the operator L, where one considers surfaces which may correspond very well to multi-valued functions u.


Shock Wave Parabolic Equation Entropy Solution Entropy Condition Ground State Solution 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Michiel Bertsch
    • 1
  • Roberta Dal Passo
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Istituto per le Applicazioni del Calcolo (IAC)RomaItaly

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