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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: <>. 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.
ISSN: 1563504X
Appears in Collections:DEMAT - Artigos publicados em periódicos

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