Existence of solutions to the Poisson equation in $L_2$-weighted spaces

Volume 37 / 2010

Joanna Renc/lawowicz, Wojciech M. Zaj/aczkowski Applicationes Mathematicae 37 (2010), 309-323 MSC: Primary 35J05; Secondary 31A30, 35J25. DOI: 10.4064/am37-3-3

Abstract

We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

Authors

  • Joanna Renc/lawowiczInstitute 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
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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