Geodesic
The solvability of extremal problems for Poisson equation and Stokes system
Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 164-170

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One consider the extremal problems for Poisson equation and Stokes system which are to minimize the $L^2$-difference solution from given function. The sufficient conditions of solvability in the Sobolev space $H^1$ are obtained. It is showed that these conditions are necessary in some cases. 
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     author = {A. A. Illarionov},
     title = {The solvability of extremal problems for {Poisson} equation and {Stokes} system},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a2/}
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A. A. Illarionov. The solvability of extremal problems for Poisson equation and Stokes system. Dalʹnevostočnyj matematičeskij žurnal, Tome 8 (2008) no. 2, pp. 164-170. http://geodesic.mathdoc.fr/item/DVMG_2008_8_2_a2/