Geodesic
Selfadjointness conditions for strongly elliptic systems of arbitrary order
Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 103-126

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Sufficient conditions are obtained for the essential selfadjointness in $\mathscr L_2(\mathbf R^n)$ of strongly elliptic systems of arbitrary even order (both semibounded and nonsemibounded) without assumptions concerning the boundedness of the leading coefficients or concerning uniform ellipticity. The conditions are formulated by means of operator inequalities and explicit restrictions on the coefficients. Bibliography: 26 titles. 
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     author = {A. G. Brusentsev and F. S. Rofe-Beketov},
     title = {Selfadjointness conditions for strongly elliptic systems of arbitrary order},
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A. G. Brusentsev; F. S. Rofe-Beketov. Selfadjointness conditions for strongly elliptic systems of arbitrary order. Sbornik. Mathematics, Tome 24 (1974) no. 1, pp. 103-126. http://geodesic.mathdoc.fr/item/SM_1974_24_1_a5/