A Free Boundary Problem: Contributions from Modern Analysis

  • José Miguel Urbano
Part of the Progress in Mathematics book series (PM, volume 202)


We exemplify the role of Free Boundary Problems as an important source of ideas in modern analysis. With the help of a model problem we illustrate the use of analytical, algebraic and geometrical techniques obtaining uniqueness of weak solutions via the use of entropy inequalities, existence through nonlinear semigroup theory, and regularity using a method, called intrinsic scaling, based on interpreting a partial differential equation in a geometry dictated by its own structure.


Weak Solution Mild Solution Free Boundary Problem Entropy Solution Entropy Inequality 
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Copyright information

© Springer Basel AG 2001

Authors and Affiliations

  • José Miguel Urbano
    • 1
  1. 1.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal

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