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 Mat. Inst. Steklova, 2013, Volume 283,Pages 115

This article is cited in 2 papers

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 $p\geq1$

V. A. Il'in^ab, A. A. Kuleshov^a

^a Lomonosov Moscow State University, Moscow, Russia
^b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: 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 $W^1_p$.

UDC: 517.9

Received in February 2013

DOI: 10.1134/S0371968513040080