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Title: An optimal pointwise Morrey-Sobolev inequality.
Authors: Ercole, Grey
Pereira, Gilberto de Assis
Keywords: Dirac delta distribution
Infinity Laplacian
Issue Date: 2020
Citation: ERCOLE, G.; PEREIRA, G. de A. An optimal pointwise Morrey-Sobolev inequality. Journal of Mathematical Analysis and Applications, v. 489, n. 1, artigo 124143, 2020. Disponível em: <>. Acesso em: 06 jul. 2022.
Abstract: Let Ω be a bounded, smooth domain of RN , N ≥ 1. For each p > N we study the optimal function s = sp in the pointwise inequality |v(x)| ≤ s(x) ∇vLp(Ω) , ∀ (x, v) ∈ Ω × W1,p 0 (Ω). We show that sp ∈ C0,1−(N/p) 0 (Ω) and that sp converges pointwise to the distance function to the boundary, as p → ∞. Moreover, we prove that if Ω is convex, then sp is concave and has a unique maximum point.
ISSN: 0022-247X
Appears in Collections:DEMAT - Artigos publicados em periódicos

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