scholarly journals A symmetry result for elliptic systems in punctured domains

2019 ◽  
Vol 18 (5) ◽  
pp. 2819-2833 ◽  
Author(s):  
Stefano Biagi ◽  
◽  
Enrico Valdinoci ◽  
Eugenio Vecchi ◽  
◽  
...  
Keyword(s):  
Elliptic Systems ◽  
Symmetry Result

scholarly journals Symmetry results for stable and monotone solutions to fibered systems of PDEs

2015 ◽  
Vol 17 (04) ◽  
pp. 1450035 ◽  
Author(s):  
Serena Dipierro ◽  
Andrea Pinamonti
Keyword(s):  
Elliptic Systems ◽  
Type Formula ◽  
Symmetry Properties ◽  
Systems Of Pdes ◽  
Symmetry Result ◽  
Monotone Solutions

We study the symmetry properties for solutions of elliptic systems of the type [Formula: see text] where x ∈ ℝm with 1 ≤ m < N, X = (x, y) ∈ ℝm × ℝN-m, and F1,…,Fn are the derivatives with respect to ξ1,…,ξn of some F = F(x,ξ1,…,ξn) such that for any i = 1,…,n and any fixed (x,ξ1,…,ξi-1,ξi+1,…,ξn) ∈ ℝm × ℝn-1 the map ξi → F(x,ξ1,…,ξi,…,ξn) belongs to C2(ℝ). We obtain a Poincaré-type formula for the solutions of the system and we use it to prove a symmetry result both for stable and for monotone solutions.

scholarly journals A symmetry result for cooperative elliptic systems with singularities

2020 ◽  
Vol 64 ◽  
pp. 621-652 ◽  
Author(s):  
Stefano Biagi ◽  
Enrico Valdinoci ◽  
Eugenio Vecchi
Keyword(s):  
Elliptic Systems ◽  
Symmetry Result
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