Symmetry properties of positive solutions for fully nonlinear elliptic systems

Autor(es)

dos Santos, Ederson Moreira ^[1] ; Nornberg, Gabrielle ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 269, n. 5, p. 4175-4191, AUG 15 2020.
• Citações Web of Science: 0

Resumo

We investigate symmetry properties of positive solutions for fully nonlinear uniformly elliptic systems, such as F-i (x, Du(i), D(2)u(i)) + f(i) (x, u(1),..., u(n), Du(i)) = 0, 1 <= i <= n, in a bounded domain Omega in R-N with Dirichlet boundary condition u(1)=..., u(n)= 0 on partial derivative Omega. Here, f(i)'s are nonincreasing with the radius r=vertical bar x vertical bar, and satisfy a cooperativity assumption. In addition, each f(i) is the sum of a locally Lipschitz with a nondecreasing function in the variable ui, and may have superlinear gradient growth. We show that symmetry occurs for systems with nondifferentiable f(i)'s by developing a unified treatment of the classical moving planes method in the spirit of Gidas-Ni-Nirenberg. We also present different applications of our results, including uniqueness of positive solutions for Lane-Emden systems in the subcritical case in a ball, and symmetry for a class of systems with natural growth in the gradient. (c) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/04000-9 - Existência e multiplicidade de soluções para problemas elípticos com crescimento quadrático no gradiente
• Beneficiário: Gabrielle Saller Nornberg
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado