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math.AP2012
Regularity of the extremal solutions associated to elliptic systems
Craig Cowan, Mostafa Fazly
We examine the two elliptic systems given by [(G)_{λ,γ} \quad -Δu = λf'(u) g(v), \quad -Δv = γf(u) g'(v) \quad in ,] and [(H)_{λ,γ} \quad -Δu = λf(u) g'(v), \quad -Δv = γf'(u)…
math.AP2012★ 1 cited
De Giorgi type results for elliptic systems
Mostafa Fazly, Nassif Ghoussoub
We consider the following elliptic system Δu =\nabla H (u) \ \ \text{in}\ \ \mathbf{R}^N, where and , and prove, under vari…