In this new coordinate system we prove an integral inequalitynwhich is related to Friedrichs' criteria for spectral discreteness in ordinary differential equations. With this integral inequality we obtain a condition for spectral discreteness of the Dirichlet operator L. When applicable, our condition has two advantages over Kreith's. L degenerates only in those directions in which the eigenvalues of (aij(x)) go to zero, and, secondly, our criterion is governed by the direction in which L de-generates most slowly.
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