Maximum principles for some quasilinear elliptic systems

• Autor(a) principal: Leonardi, Salvatore
• Data de Publicação: 2020
• Outros Autores: Leonetti, Francesco, Pignotti, Cristina, Rocha, Eugénio, Staicu, Vasile
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/25838
• topic: Elliptic system; Maximum principle; r-staircase support

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