The Fundamental Estimate

  • Gianni Dal Maso
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 8)


We have seen in Examples 16.13 and 16.14 that, in general, the \( \bar{\Gamma } \)-limit of a sequence of measures is not a measure. In this chapter we study a condition, called the fundamental estimate, which plays a central role in the theorems about \( \bar{\Gamma } \)-limits of measures. Indeed, we shall prove that the \( \bar{\Gamma } \)-limit of a sequence (F h ) of increasing functionals on L p (Ω) × A is a measure, provided that all functionals of the sequence are measures and satisfy the fundamental estimate uniformly with respect to h.


Open Subset Convex Combination Lower Semicontinuous Radon Measure Integral Functional 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Gianni Dal Maso
    • 1
  1. 1.International School for Advanced Studies (SISSA)TriesteItaly

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