A differential operator with constant coefficients is hypoelliptic if and only if its solution space is of finite functional dimension. We extend this property to operators with variable coefficient. We prove that an equally strong differential operator with variable coefficients has the same property. In addition, we extend the Zielezny’s result to operators with variable coefficients; prove that an operator with analytic coefficients on ℝn is elliptic if and only if locally the functional dimension of its solution space is the same as the Euclidean dimension n.
Functional Dimension of Solution Space of Differential Operators of Constant Strength,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 14,
1, Article 26.
Available at: https://digitalcommons.pvamu.edu/aam/vol14/iss1/26