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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. A. Kondratev, T. G. Pletneva, S. D. Eidelman, “O polozhitelnykh resheniyakh ellipticheskikh uravnenii”, Matem. sb., 85 (127) (1971), 586–609 | MR

[2] V. A. Kondratev, T. G. Pletneva, S. D. Eidelman, “Polozhitelnye resheniya evolyutsionnykh kvaziellipticheskikh uravnenii”, Matem. sb., 89 (191) (1972), 16–45 | MR

[3] V. A. Kondratev, S. D. Eidelman, “Polozhitelnye resheniya lineinykh uravnenii s chastnymi proizvodnymi”, Trudy mosk. matem. ob-va, XXXI (1974), 85–145 | MR

[4] O. A. Oleinik, E. V. Radkevich, “Uravnenie vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Itogi nauki. Seriya matematika. Matem. analiz. 1969, VINITI, Moskva, 1971, 7–252 | MR