Please use this identifier to cite or link to this item:
http://www.repositorio.ufop.br/jspui/handle/123456789/10560
Title: | Computing the best constant in the Sobolev inequality for a ball. |
Authors: | Ercole, Grey Espírito Santo, Júlio César do Martins, Eder Marinho |
Issue Date: | 2017 |
Citation: | ENCOLE, G.; ESPÍRITO SANTO, J. C do.; MARTINS, E. M. Computing the best constant in the Sobolev inequality for a ball. Applicable Analysis, v. 1, p. 1-17, 2018. Disponível em: <https://www.tandfonline.com/doi/full/10.1080/00036811.2017.1422723>. Acesso em: 16 jun. 2018. |
Abstract: | Let B1 be the unit ball of R N , N ≥ 2, and let p ? = N p/(N − p) if 1 < p < N and p ? = ∞ if p ≥ N. For each q ∈ [1, p? ) let wq ∈ W1,p 0 (B1) be the positive function such that kwqkLq(B1) = 1 and λq(B1) := min ( k∇uk p Lp(B1) kuk p Lq(B1) : 0 6≡ u ∈ W1,p 0 (B1) ) = k∇wqk p Lp(B1) . In this paper we develop an iterative method for obtaining the pair (λq(B1), wq), starting from w1. Since w1 is explicitly known, the method is computationally practical, as our numerical tests show. 2010 Mathematics Subject Classification. 34L16; 35J25; 65N25 Keywords: Best Sobolev constant; extremal functions; inverse iteration method; p-Laplacian. |
URI: | http://www.repositorio.ufop.br/handle/123456789/10560 |
metadata.dc.identifier.uri2: | https://www.tandfonline.com/doi/full/10.1080/00036811.2017.1422723 |
ISSN: | 1563504X |
Appears in Collections: | DEMAT - Artigos publicados em periódicos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
ARTIGO_ComputingBestConstant.pdf Restricted Access | 817,67 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.