The smoothness of regular equations according to parameter

G. А. Karapetyan

Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (1988), pp. 21-29

Résumé

In the article the solution of smoothness of one of the classes of hypo elliptic equations according to $\lambda$ parameter has been proved. The following has been proved particularly. For example, if we have the equation $P(\lambda, D)u=f$. Let’s mark by $N(\lambda)$ the set of solutions of equation $P(\lambda, D)u=0$ from class $W_2^H(R^n)$. If the dimension of $N(\lambda)$ does not depend on $\lambda,$ then all the solutions of equation $P(\lambda, D)u = f$ that are orthogonal to $N(\lambda)$ are infinitely differentiable by $(x, \lambda)$.