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Bounded solutions of elliptic equations as multipliers in spaces of differentiable functions. (Russian) Zbl 0601.35023
Author’s summary: It is shown that bounded solutions of second order linear elliptic differential equations are multipliers in certain weighted Hilbert spaces of pairs of such spaces. The role of the weight is played by a power of the distance to the boundary of the domain or a function of the distance. This function is subjected a condition which is necessary and sufficient for the solution to be in the corresponding class of multipliers.
Reviewer: Ya.Rojtberg

MSC:
35J15Second order elliptic equations, general
35B35Stability of solutions of PDE
46E20Hilbert spaces of continuous, differentiable or analytic functions