Local properties of solutions of elliptic partial differential equations

  • A. P. Calderón
  • A. Zygmund
Part of the Mathematics and Its Applications book series (MAEE, volume 41)


The purpose of this paper is to establish pointwise estimates for solutions of elliptic partial differential equations and systems. The results presented here differ from the familiar ones in that they give information about the behavior of solutions at individual points. More specifically, we obtain two kinds of results. On the one hand, we establish inequalities for solutions and their derivatives at isolated individual points. On the other, we also obtain results of the „almost everywhere“ type. Theorems 1 and 2 below summarize the main results.


Compact Support Taylor Expansion Differentiable Function Inverse Fourier Transform Singular Integral Operator 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • A. P. Calderón
    • 1
  • A. Zygmund
    • 1
  1. 1.ChicagoUSA

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