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Title: Maximum principles for some quasilinear elliptic systems
Author: Leonardi, Salvatore
Leonetti, Francesco
Pignotti, Cristina
Rocha, Eugénio
Staicu, Vasile
Keywords: Elliptic system
Maximum principle
r-staircase support
Issue Date: May-2020
Publisher: Elsevier
Abstract: We give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that off-diagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane
Peer review: yes
DOI: 10.1016/
ISSN: 0362-546X
Publisher Version:
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FAAG - Artigos

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