Existence of solutions to the Poisson equation in $L_p$-weighted spaces

Volume 37 / 2010

Joanna Rencławowicz, Wojciech M. Zaj/aczkowski Applicationes Mathematicae 37 (2010), 1-12 MSC: Primary 35J05; Secondary 31A30, 35J25. DOI: 10.4064/am37-1-1

Abstract

We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_p$, $ p\geq 3$, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted $L_2$ space.

Authors

  • Joanna RencławowiczInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    e-mail
  • Wojciech M. Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-956 Warszawa, Poland
    and
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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