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~$p\geq1$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 115-120.

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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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     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 = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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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~$p\geq1$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 115-120. http://geodesic.mathdoc.fr/item/TM_2013_283_a7/

[1] Ilin V.A., Kuleshov A.A., “Obobschennye resheniya volnovogo uravneniya iz klassov $L_p$ i $W_p^1$ pri $p\geq 1$”, DAN, 446:4 (2012), 374–377 | Zbl

[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

[3] Ilin V.A., Kuleshov A.A., “Kriterii prinadlezhnosti klassu $W_p^1$ obobschennogo iz klassa $L_p$ resheniya volnovogo uravneniya”, DAN, 447:1 (2012), 15–17 | Zbl

[4] Ilin V.A., Kuleshov A.A., “Ob opredelenii obobschennogo iz klassa $L_p$ resheniya smeshannoi zadachi dlya volnovogo uravneniya cherez integralnoe tozhdestvo”, DAN, 447:3 (2012), 247–251 | Zbl

[5] Ilin V.A., Kuleshov A.A., “O nekotorykh svoistvakh obobschennykh reshenii volnovogo uravneniya iz klassov $L_p$ i $W_p^1$ pri $p\geq 1$”, Dif. uravneniya, 48:11 (2012), 1493–1500 | Zbl

[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