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Singular quasilinear elliptic systems and H\"older regularity

Giacomoni, Jacques, Schindler, Ian and Takac, Peter (2015) Singular quasilinear elliptic systems and H\"older regularity. Differential and Integral Equations. An International Journal for Theory & Applications, vol. 20 (n° 3/4). pp. 259-298.

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We investigate the following singular quasilinear elliptic system,
−Δpu−Δqv=1ua1vb1 in Ω;u|∂Ω=1va2ub2 in Ω;v|∂Ω=0,u>0 in Ω,=0,v>0 in Ω,⎫⎭⎬⎪⎪
where Ω is an open bounded domain with smooth boundary, 1<p,q<∞, and the numbers a1,a2,b1,b2>0 satisfy certain upper bounds. We employ monotonicity methods in order to prove the existence and uniqueness of a pair of positive solutions to (P). While following a standard fixed point approach with ordered pairs of sub- and super solutions, we need to prove a new regularity result of independent interest for solution pairs to problem (P) in C0,β(Ω⎯⎯⎯⎯⎯) with some β∈(0,1).

Item Type: Article
Language: English
Date: 2015
Refereed: Yes
Divisions: Institut de mathématiques de Toulouse, TSE-R (Toulouse)
Site: UT1
Date Deposited: 08 Mar 2018 13:42
Last Modified: 26 Feb 2020 15:49

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