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

Joanna Rencławowicz; Wojciech M. Zajączkowski

doi:10.4064/am37-1-1

Geodesic

Parcourir par

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.

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

Résumé

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

Affiliations des auteurs :

Joanna Rencławowicz ¹ ; Wojciech M. Zajączkowski ²

@article{10_4064_am37_1_1,
     author = {Joanna Renc{\l}awowicz and Wojciech M. Zaj\k{a}czkowski},
     title = {Existence of solutions to the {Poisson} equation  in $L_p$-weighted spaces},
     journal = {Applicationes Mathematicae},
     pages = {1--12},
     publisher = {mathdoc},
     volume = {37},
     number = {1},
     year = {2010},
     doi = {10.4064/am37-1-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am37-1-1/}
}

TY  - JOUR
AU  - Joanna Rencławowicz
AU  - Wojciech M. Zajączkowski
TI  - Existence of solutions to the Poisson equation  in $L_p$-weighted spaces
JO  - Applicationes Mathematicae
PY  - 2010
SP  - 1
EP  - 12
VL  - 37
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am37-1-1/
DO  - 10.4064/am37-1-1
LA  - en
ID  - 10_4064_am37_1_1
ER  -

%0 Journal Article
%A Joanna Rencławowicz
%A Wojciech M. Zajączkowski
%T Existence of solutions to the Poisson equation  in $L_p$-weighted spaces
%J Applicationes Mathematicae
%D 2010
%P 1-12
%V 37
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am37-1-1/
%R 10.4064/am37-1-1
%G en
%F 10_4064_am37_1_1

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. http://geodesic.mathdoc.fr/articles/10.4064/am37-1-1/

Cité par Sources :