Giacomoni, Jacques, Schindler, Ian and Takáč, 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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Abstract

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
Subjects: G- MATHEMATIQUES
Divisions: Institut de mathématiques de Toulouse, TSE-R (Toulouse)
Site: UT1
Date Deposited: 08 Mar 2018 13:42
Last Modified: 30 Aug 2023 13:47
URI: https://publications.ut-capitole.fr/id/eprint/25103
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