On the moving plane method for singular solutions to semilinear elliptic equations
On the moving plane method for singular solutions to semilinear elliptic equations
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DOI：
10.1016/j.matpur.2016.10.012
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发表时间：
2017-07
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影响因子：
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通讯作者：
B. Sciunzi
中科院分区：
文献类型：
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作者：
B. Sciunzi
考虑了方程− Δ u= f（x，u）在Ω <$r中的弱正解，其中u= 0在Ω <$Ω上.在对f和奇异集Γ的适当假设下，利用移动平面方法证明了对称凸域上解的对称性和单调性.与类似的论点，我们也考虑的情况下，当域是整个空间和非线性最关键的增长。
We consider positive weak solutions to− Δ u= f (x, u) in Ω∖ Γ with u= 0 on∂ Ω. We prove symmetry and monotonicity properties of the solutions in symmetric convex domains via the moving plane method, under suitable assumptions on f and on the singular set Γ. With similar arguments we also consider the case when the domain is the whole space and the nonlinearity has at most critical growth.