Geodesic
Interior estimates for solutions of linear elliptic inequalities
Izvestiya. Mathematics , Tome 85 (2021) no. 1, pp. 92-110

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We study the wedge of solutions of the inequality $A(u) \geqslant 0$, where $A$ is a linear elliptic operator of order $2m$ acting on functions \linebreak of $n$ variables. We establish interior estimates of the form $\|u; W_p^{2m-1}(\omega)\| \leqslant C(\omega,\Omega) \|u;L(\Omega)\|$ for the elements of this wedge, where $\omega$ is a compact subdomain of $\Omega$, $W_p^{2 m-1}(\omega)$ is the Sobolev space, $p (n-1)$, $L(\Omega)$ is the Lebesgue space of integrable functions, and the constant $C(\omega,\Omega)$ is independent of $u$.
Keywords: wedge, function, elliptic inequality, Banach space.
Mots-clés : norm 
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     author = {V. S. Klimov},
     title = {Interior estimates for solutions of linear elliptic inequalities},
     journal = {Izvestiya. Mathematics },
     pages = {92--110},
     publisher = {mathdoc},
     volume = {85},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_1_a3/}
}
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V. S. Klimov. Interior estimates for solutions of linear elliptic inequalities. Izvestiya. Mathematics , Tome 85 (2021) no. 1, pp. 92-110. http://geodesic.mathdoc.fr/item/IM2_2021_85_1_a3/