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- Asadzadeh, Mohammad, 1952, et al.
(författare)
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The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain
- 1992
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Ingår i: Mathematical Models and Methods in Applied Science. ; 2:3, s. 317-338
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Tidskriftsartikel (refereegranskat)abstract
- We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
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| 3. |
- Brenner, Philip, 1941, et al.
(författare)
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Nonlinear Maps between Besov and Sobolev spaces
- 2010
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Ingår i: Annales de la Faculte des Sciences de Toulouse. - : Cellule MathDoc/CEDRAM. - 0240-2963 .- 2258-7519. ; 19:1, s. 105-120
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Our main result shows that for a large class of nonlinear local mappings between Besov and Sobolev space, interpolation is an exceptional low dimensional phenomenon. This extends previous results by Kumlin [13] from the case of analytic mappings to Lipschitz and Hölder continuous maps (Corollaries 1 and 2), and which go back to ideas of the late B.E.J. Dahlberg [8].
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| 6. |
- Horiuchi, Toshio, et al.
(författare)
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On the Caffarelli-Kohn-Nirenberg-type inequalities involving critical and supercritical weights
- 2012
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Ingår i: Kyoto Journal of Mathematics. - : Duke University Press. - 2156-2261 .- 2154-3321. ; 52:4, s. 661-742
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Tidskriftsartikel (refereegranskat)abstract
- The main purpose of this article is to establish the Caffarelli–Kohn– Nirenberg-type (CKN-type) inequalities for all α∈R and to study the related matters systematically. Roughly speaking, we discuss the characterizations of the CKN-type inequalities for all α∈R as the variational problems, the existence and nonexistence of the extremal solutions to these variational problems in proper spaces, and the exact values and the asymptotic behaviors of the best constants in both the noncritical case and the critical case. In the study of the CKN-type inequalities, the presence of weight functions on both sides prevents us from employing effectively the so-called spherically symmetric rearrangement. Further the invariance of Rn by the group of dilatations creates some possible loss of compactness. As a result we see that the existence of extremals, the values of best constants, and their asymptotic behaviors essentially depend upon the relations among parameters in the inequality.
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| 8. |
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| 9. |
- Horiuchi, T., et al.
(författare)
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The Caffarelli-Kohn-Nirenberg type inequalities involving critical and supercritical weights
- 2012
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Ingår i: Proceedings of the Japan Academy Series a-Mathematical Sciences. - : Project Euclid. - 0386-2194. ; 88:1, s. 1-6
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Tidskriftsartikel (refereegranskat)abstract
- The main purpose of this article is to establish the CKN-type inequalities for all alpha is an element of R and to study the relating matters systematically. Roughly speaking, we shall discuss about the characterizations of the CKN-type inequalities for all alpha is an element of R as the variational problems, the existence and nonexistence of the extremal solutions to these variational problems in proper spaces, the exact values and the assymptotic behaviors of the best constants S(p, q, alpha) and C(p, q).
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| 10. |
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