Abstract
We show that there are no entire, positive, stable solutions in ℝn of the Euler equation corresponding to the singular variational integral\(\smallint u^\alpha \sqrt {1 + |Du|^2 } dx\),α>0, ifα+n<5.236.... Furthermore we prove a related result for smooth boundaries of leastα-energy ∫|xn+1|α|DϕU| in ℝn+1.
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