Differentiability and growth of solutions of partial differential equations
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Regularity problems are studied for a PDO P(D) with constant coefficients using a new variant of the parametrix-method. A new Characterization of the index of hypoellipticity r and a pointwise uniquness theorem for the Cauchy-problem is given. For semielliptic P(D) the functional dimension of C p ∞ (R n ) is proved to be ¦r¦. The equation P(D)g=f Is solved with distributions with part. bounded support.
KeywordsFundamental Solution Elementary Solution Constant Coefficient Finite Type Linear Partial Differential Equation
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