Geodesic
Reverse Inequalities for Subelliptic Functions
Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 525-539.

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We study a wedge $\mathscr{K}(A)$ of solutions of the inequality $A(u) \ge 0$, where $A$ is a linear elliptic operator of order $2m$. For the elements of the wedge, we establish an interior estimate of the form $$ \|u;H_1^{2m}(\omega)\| \le C(\omega,\Omega)\|u;L(\Omega)\|, $$ where $\omega$ is a compact subset of $\Omega$, $H_1^{2 m}(\omega)$ is the Nikol'skii space, $L(\Omega)$ is the Lebesgue space of integrable functions, and the constant $C(\omega,\Omega)$ is independent of the function $u$. Similar estimates that hold up to the boundaries are proved for the functions from $\mathscr{K}(A)$ satisfying the boundary conditions.
Keywords: wedge, function, elliptic inequality, Banach space.
Mots-clés : norm 
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V. S. Klimov. Reverse Inequalities for Subelliptic Functions. Matematičeskie zametki, Tome 111 (2022) no. 4, pp. 525-539. http://geodesic.mathdoc.fr/item/MZM_2022_111_4_a4/

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