Geodesic
On the normal solvability of elliptic equations in the Holder space functions on plane
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 1, pp. 3-13

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The uniformly elliptic equation $$ Lw\equiv w_{\overline{z}}+q_1(z)w_z+q_2(z)\overline{w}_{\overline{z}}+a(z)w+b(z)\overline{w}=f(z) $$ with coefficients in the Holder space functions $C_\alpha$ on plane are considered. The equivalency following assertions is established: a) the operator $L: C_\alpha^1\to C_\alpha$ is $n$-normal; b) the a priori estimate $$ ||w||_{1,\alpha}\leqslant M(||Lw||_\alpha+\max_{|z|\leqslant1}|w(z)|), $$ is valid; c) a corresponding limit equations has only the zero solution in $C^1_\alpha$. 
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     author = {S. Baizaev and E. Muhamadiev},
     title = {On the normal solvability of elliptic equations in the {Holder} space functions on plane},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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S. Baizaev; E. Muhamadiev. On the normal solvability of elliptic equations in the Holder space functions on plane. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 1, pp. 3-13. http://geodesic.mathdoc.fr/item/VNGU_2006_6_1_a0/