Titlebook: Linear Partial Differential Operators; Lars Hörmander Book 1964Latest edition Springer-Verlag Berlin Heidelberg 1964 analysis.differential

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The Cauchy problem (constant coefficients)To solve the Cauchy problem for a differential operator .(.) with data on a plane <.>= 0, where 0 ≠ . ∈R., means, roughly speaking, to find a solution . of the equation.where . is given, so that for another given function ϕ..

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Differential equations which have no solutionsIn Chapter III we proved that a differential equation with constant coefficients can be solved for an arbitrary right-hand side ., at least in relatively compact open subsets of the open set where . is defined. It was discovered rather recently by H. . [1] that the situation is completely different when the coefficients are variable.

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