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Fritz John pp 385-388 | Cite as

A Note on “Improper” Problems in Partial Differential Equations

  • Fritz John
Chapter
Part of the Contemporary Mathematicians book series (CM)

Abstract

In the theory of partial differential equations one encounters problems which consist in determining a solution u of an equation from certain data f. Following the discussion of Hadamard1 and of Courant-Hilbert2 one is led to consider a problem of this type only then as “proper” or “correctly set” if it meets certain requirements. One requires namely that there shall exist a class γ of data f and a class Γ of solutions u, such that for every f in γ
  1. 1)

    there exists a corresponding u in Γ,

     
  2. 2)

    u is determined uniquely,

     
  3. 3)

    u depends “continuously” on f.

     

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Fritz John

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