Geodesic
Existence of solutions to the Poisson equation in $L_2$-weighted spaces
Joanna Rencławowicz1 ; Wojciech M. Zajączkowski2
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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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. http://geodesic.mathdoc.fr/articles/10.4064/am37-3-3/

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