A Note on “Improper” Problems in Partial Differential Equations
Part of the Contemporary Mathematicians book series (CM)
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
there exists a corresponding u in Γ,
u is determined uniquely,
u depends “continuously” on f.
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© Springer Science+Business Media New York 1985