Geodesic
On the summability of positive solutions of partial differential equations of arbitrary order in a~neighborhood of a~characteristic manifold
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 521-531

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A nonnegative solution of the equation $\sum_{|\alpha|\leqslant m}a_\alpha(x)D^\alpha u=0$ is considered in an arbitrary domain $G$ with smooth boundary $\Gamma$. The surface $\Gamma$ can contain a characteristic manifold $\Gamma_0$. Conditions on $\Gamma_0$ are obtained ensuring that $\int_Gu\,dx$ is always finite. These conditions turn out to be best possible. Bibliography: 4 titles. 
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     author = {V. A. Kondrat'ev and S. D. \`Eidel'man},
     title = {On the summability of positive solutions of partial differential equations of arbitrary order in a~neighborhood of a~characteristic manifold},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {28},
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V. A. Kondrat'ev; S. D. Èidel'man. On the summability of positive solutions of partial differential equations of arbitrary order in a~neighborhood of a~characteristic manifold. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 521-531. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a5/