Geodesic
Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with $p\geq1$
Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 115-120 
V. A. Il'in; A. A. Kuleshov. Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with $p\geq1$. Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 115-120. http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a7/
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     author = {V. A. Il'in and A. A. Kuleshov},
     title = {Necessary and sufficient conditions for a~generalized solution to the initial-boundary value problem for the wave equation to belong to $W^1_p$ with~$p\geq1$},
     journal = {Informatics and Automation},
     pages = {115--120},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish necessary and sufficient conditions on the boundary function under which a generalized solution to the initial–boundary value problem for the wave equation with boundary conditions of the first kind belongs to $W^1_p$.

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[2] Ilin V.A., Kuleshov A.A., “Kriterii prinadlezhnosti klassu $L_p$ pri $p\geq 1$ obobschennogo resheniya smeshannoi zadachi dlya volnovogo uravneniya”, DAN, 446:6 (2012), 612–614 | Zbl

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[6] Ilin V.A., Kuleshov A.A., “Neobkhodimoe i dostatochnoe uslovie prinadlezhnosti klassu $L_p$ pri $p\geq 1$ obobschennogo resheniya smeshannoi zadachi dlya volnovogo uravneniya”, Dif. uravneniya, 48:12 (2012), 1607–1611 | Zbl