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Sobolev Spaces and Pseudo-Differential Operators

  • Felipe Linares
  • Gustavo Ponce
Chapter
Part of the Universitext book series (UTX)

In this chapter we will give a brief introduction to the classical Sobolev spaces Hs(Rn). Sobolev spaces measure the differentiability of functions in L2(Rn) and they are a fundamental tool in the study of partial differential equations.We also will list some basic facts of the theory of pseudo-differential operators without proof. This will be useful to study smoothness properties of solutions of dispersive equations.

Keywords

Sobolev Space Pseudodifferential Operator Principal Symbol Distribution Sense Leibniz Rule 
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-Verlag New York 2009

Authors and Affiliations

  1. 1.Instituto Nacional deMatemática Pura e Aplicada (IMPA)Rio de Janeiro-RJBrazil
  2. 2.Department MathematicsUniversity of CaliforniaSanta BarbaraUSA

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