Necessity of Parameter-ellipticity for Multi-order Systems of Differential Equations
In this paper we investigate parameter-ellipticity conditions for multi-order systems of differential equations on a bounded domain.Unde r suitable assumptions on smoothness and on the order structure of the system, it is shown that parameter-dependent a priori estimates imply the conditions of parameter-ellipticity, i.e., interior ellipticity, conditions of Shapiro- Lopatinskii type, and conditions of Vishik-Lyusternik type.T he mixed-order systems considered here are of general form; in particular, it is not assumed that the diagonal operators are of the same order.Th is paper is a continuation of an article by the same authors where the sufficiency was shown, i.e., a priori estimates for the solutions of parameter-elliptic multi-order systems were established.
KeywordsParameter-ellipticity multi-order systems a priori estimates
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