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Calculus Inequalities

  • Mi-Ho Giga
  • Yoshikazu Giga
  • Jürgen Saal
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 79)

Abstract

In this section we introduce the Nash inequality and its generalized version, the Gagliardo–Nirenberg inequality. Roughly speaking, these inequalities provide estimates for an integral of a function by its derivatives, a tool that is very helpful not only in the analysis of the vorticity equations as demonstrated in Chapter 2, but in the analysis of nonlinear PDE in general.

Keywords

Heat Equation Bounded Linear Operator Sobolev Inequality Singular Integral Operator Lorentz Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoMeguro-kuJapan
  2. 2.Technische Universität Darmstadt Center of Smart InterfacesDarmstadtGermany

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