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Qualitative properties of solutions to elliptic singular problems

Berhanu, Shiferaw and Gladiali, Francesca Maria and Porru, Giovanni (1999) Qualitative properties of solutions to elliptic singular problems. Journal of Inequalities and Applications, Vol. 3 (4), p. 313-330. eISSN 1029-242X. Article.

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DOI: 10.1155/S1025583499000223


We investigate the singular boundary value problem Δu+u−γ=0 in D, u=0 on ∂D, where γ>0. For γ>1, we find the estimate |u(x)−b0δ2/(γ+1)(x)| <βδ(γ−1)/(γ+1)(x), where b0 depends on γ only, δ(x) denotes the distance from x to ∂D and is β suitable constant. For γ>0, we prove that the function u(1+γ)/2 is concave whenever D is convex. A similar result is well known for the equation Δu+up=0, with 0≤p≤1. For p=0, p=1 and γ≥1 we prove convexity sharpness results.

Item Type:Article
ID Code:5255
Uncontrolled Keywords:Singular equations, boundary behaviour, convexity
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 03 Istituti > Matematica e fisica
Publisher:Hindawi Publishing Corporation
Copyright Holders:© 1999 Hindawi Publishing Corporation
Deposited On:16 Dec 2010 10:11

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