Fritz John pp 460-461 | Cite as

Commentary on [39] and [47]

  • L. Hörmander
Part of the Contemporary Mathematicians book series (CM)


On page 553 in [47] John remarks that “there appears to be a connection between well-behaved character of a problem and regularity of the solution for regular data”. An example of this is given for the wave equation. u tt - u xx - u yy = 0 in R 3. On one hand, the continuation of solutions from a cylinder Φ = {(x, y, t); x 2 + y 2< r 2} to the complement is shown to be only very weakly continuous. On the other hand, a solution is constructed which is analytic in Φ, of class C m exactly on ∂Φ and of class C m +1 exactly in the complement of Φ. John comments on page 574: “What is remarkable is that this cylinder is not a characteristic surface for the differential equation. Apparently not all types of singularities propagate along characteristic surfaces.”


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© Springer Science+Business Media New York 1985

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  • L. Hörmander

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