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Cited by 3 publications
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“…For p = 1, because of lack of compactness, the problem remained open. Using new fixed point results for the weak topology, obtained in the work of Latrach et al, 7 the problem was solved for bounded velocities in Latrach and Zeghal, 8 and afterwards, the results were extended to unbounded velocities in Boumhamdi et al 9 Note also that in Latrach et al, 10 existence results for a mono-energetic singular transport equation on L 1 -spaces in slab geometry were discussed for specular reflections and periodic boundary conditions. Our objective here is to complete the analysis started in the works.…”
Section: Introductionmentioning
confidence: 99%
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“…For p = 1, because of lack of compactness, the problem remained open. Using new fixed point results for the weak topology, obtained in the work of Latrach et al, 7 the problem was solved for bounded velocities in Latrach and Zeghal, 8 and afterwards, the results were extended to unbounded velocities in Boumhamdi et al 9 Note also that in Latrach et al, 10 existence results for a mono-energetic singular transport equation on L 1 -spaces in slab geometry were discussed for specular reflections and periodic boundary conditions. Our objective here is to complete the analysis started in the works.…”
Section: Introductionmentioning
confidence: 99%
“…Our objective here is to complete the analysis started in the works. 6,[8][9][10] We discuss the existence of solutions to the multidimensional problems (1) and (2) assuming that the collision frequency (·) and the collision operator satisfy the hypotheses (i) and (ii). The first one means that the singularities of the collision frequency are contained in a set of zero Lebesgue measure, while it implies that K is not, as usually bounded in L p (D × R n , dxdv), but it is solely bounded from the weighted space L p (D × R n , (v)dxdv) into L p (D × R n , dxdv).…”
Section: Introductionmentioning
confidence: 99%
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