Geodesic
Inverse boundary problem for the thin plates bending equation with the additional integral condition
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 83-101

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In the paper an inverse boundary value problem for the thin plates bending equation with the additional integral condition of the first kind is investigated. First, the initial problem is reduced to the equivalent problem, for which the theorem of existence and uniqueness of solutions is proved. Then, using these facts, the existence and uniqueness of the classical solution of initial problem is proved. 
@article{DVMG_2013_13_1_a7,
     author = {Ya. T. Megraliev},
     title = {Inverse boundary problem for the thin plates bending equation with the additional integral condition},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {83--101},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a7/}
}
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Ya. T. Megraliev. Inverse boundary problem for the thin plates bending equation with the additional integral condition. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 1, pp. 83-101. http://geodesic.mathdoc.fr/item/DVMG_2013_13_1_a7/