Geodesic
Existence of solutions to the Poisson equation in $L_p$-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 Cybernetics Faculty Military University of Technology Kaliskiego 2 00-908 Warszawa, Poland
Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 1-12 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am37-1-1
Keywords: examine poisson equation boundary conditions cylinder weighted space geq type weight positive power distance distinguished plane prove existence solutions result existence 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 Cybernetics Faculty 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 $L_p$-weighted spaces. Applicationes Mathematicae, Tome 37 (2010) no. 1, pp. 1-12. doi: 10.4064/am37-1-1

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