Geodesic
Solvability of the Poisson equation in weighted Sobolev spaces
Wojciech M. Zajączkowski1
1 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. 3, pp. 325-339 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier–Stokes equations which are close to axially symmetric solutions.
DOI : 10.4064/am37-3-4
Keywords: paper prove existence solutions poisson equation weighted sobolev spaces where weight distance distinguished axis raised negative power therefore looking solutions which vanish sufficiently fast near axis result useful proof existence global regular solutions navier stokes equations which close axially symmetric solutions

Wojciech M. Zajączkowski 1

1 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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Wojciech M. Zajączkowski. Solvability of the Poisson equation in weighted Sobolev spaces. Applicationes Mathematicae, Tome 37 (2010) no. 3, pp. 325-339. doi: 10.4064/am37-3-4

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