PARTITION OF UNITY AND THE STRONG ELLIPTICITY PROBLEM FOR FUNCTIONAL DIFFERENTIAL OPERATORS

摘要

The first result on the strong ellipticity for systems of differential equations with constant coefficient was obtained by Vishik [9]. Garding [3] used partitions of unity to obtain sufficient conditions for the strong ellipticity of partial differential equations with variable coefficients. One can find other results about strong ellipticity in [1, 2, 5]. Later, Skubachevskii [8] used a special partition of unity to obtain sufficient conditions of the strong ellipticity of differential difference equations with variable coefficients. This special partition of unity commutes with difference operators.