Geodesic
A boundary value problem for higher order elliptic equations in many connected domain on the plane
Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 51-58

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For the elliptic equation of $2l$th order with constant (and leading) coefficients boundary value a problem with normal derivatives of the $(k_j-1)-$order, $j=1,\ldots,l$ considered. Here $1\le k_1 \ldots k_l\le 2l$. When $k_j=j$ it moves to the Dirichlet problem, and when $k_j = j + 1$ it corresponds to the Neumann problem. The sufficient condition of the Fredholm problem and index formula are given. 
@article{VMJ_2017_19_3_a5,
     author = {A. P. Soldatov},
     title = {A boundary value problem for higher order elliptic equations in many connected domain on the plane},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {51--58},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a5/}
}
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A. P. Soldatov. A boundary value problem for higher order elliptic equations in many connected domain on the plane. Vladikavkazskij matematičeskij žurnal, Tome 19 (2017) no. 3, pp. 51-58. http://geodesic.mathdoc.fr/item/VMJ_2017_19_3_a5/