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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 ≥ 1

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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 .

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References

  1. V. A. Il’in and A. A. Kuleshov, “Generalized solutions of the wave equation in the classes L p and W 1p with p ≥ 1,” Dokl. Akad. Nauk 446(4), 374–377 (2012) [Dokl. Math. 86 (2), 657–660 (2012)].

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  2. V. A. Il’in and A. A. Kuleshov, “A criterion for the membership in the class L p with p ≥ 1 of the generalized solution to the mixed problem for the wave equation,” Dokl. Akad. Nauk 446(6), 612–614 (2012) [Dokl. Math. 86 (2), 688–690 (2012)].

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  6. V. A. Il’in and A. A. Kuleshov, “Necessary and sufficient condition for the generalized solution of a mixed problem for the wave equation to belong to the class L p for p ≥ 1,” Diff. Uravn. 48(12), 1607–1611 (2012) [Diff. Eqns. 48, 1572–1576 (2012)].

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    V. A. Il’in & A. A. Kuleshov

  2. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. A. Il’in

Authors
  1. V. A. Il’in
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  2. A. A. Kuleshov
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Correspondence to V. A. Il’in.

Additional information

Original Russian Text © V.A. Il’in, A.A. Kuleshov, 2013, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Vol. 283, pp. 115–120.

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Il’in, V.A., Kuleshov, A.A. 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 ≥ 1. Proc. Steklov Inst. Math. 283, 110–115 (2013). https://doi.org/10.1134/S0081543813080087

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  • DOI: https://doi.org/10.1134/S0081543813080087

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