Equations with Lipschitz Nonlinearities

  • Viorel Barbu
  • Giuseppe Da Prato
  • Michael Röckner
Part of the Lecture Notes in Mathematics book series (LNM, volume 2163)


We start here by studying the porous media equation problem (1.1) when \(\beta: \mathbb{R} \rightarrow \mathbb{R}\) is monotonically increasing and Lipschitz continuous. The main reason is that general maximal monotone graphs β can be approximated by their Yosida approximations β ε which are Lipschitz continuous and monotonically increasing. So, several estimates proved in this chapter will be exploited later for studying problems with more general β.


Lipschitz Nonlinearities Yosida Approximation Maximal Monotone Independent Real Brownian Motions Nonlinear Maximal Monotone Operators 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Viorel Barbu
    • 1
  • Giuseppe Da Prato
    • 2
  • Michael Röckner
    • 3
  1. 1.Department of MathematicsAl. I. Cuza University & Octav Mayer Institute of Mathematics of the Romanian AcademyIasiRomania
  2. 2.Classe di ScienzeScuola Normale Superiore di PisaPisaItaly
  3. 3.Department of MathematicsUniversity of BielefeldBielefeldGermany

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