Results Motivated by Partial Differential Equations
The Cauchy-Kowalewsky theorem is perhaps the most general result in the theory of partial differential equations. The theory needed to state and prove a basic version of that theorem is entirely elementary. Similarly, the specific constant coefficient partial differential equations of mathematical physics—Poisson’s equation, the heat equation, and the wave equation—can be dealt with by specific elementary methods. On the other hand, the development of the general theory of linear partial differential operators with constant coefficients is tied to the more advanced and abstract theory of distributions introduced by Laurent Schwartz (see [SL 50]).
KeywordsPartial Differential Equation Nonnegative Integer Real Root Dirac Mass Real Polynomial
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