On the summability of positive solutions of partial differential equations of arbitrary order in a neighborhood of a characteristic manifold

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.
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