Geodesic
Existence of solutions to the Poisson equation in $L_2$-weighted spaces
Joanna Rencławowicz 1   ; Wojciech M. Zajączkowski 2
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
2 Institute 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
Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 309-323 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am37-3-3
Keywords: consider poisson equation dirichlet neumann boundary conditions weighted sobolev spaces weight positive power distance distinguished plane prove existence solutions suitably defined weighted space

Joanna Rencławowicz  1   ; Wojciech M. Zajączkowski  2

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
2 Institute 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 
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Joanna Rencławowicz; Wojciech M. Zajączkowski. Existence of solutions to the Poisson equation in $L_2$-weighted spaces. Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 309-323. doi: 10.4064/am37-3-3

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