扭转和基态最大值：接近但不相同
Torsion and ground state maxima: close but not the same
摘要：
凸区域上半线性泊松方程正解的极大点的位置是否与非线性项的形式无关？西玛和德里克为这个令人惊讶的猜想找到了某些证据。我们构造了半圆盘上的反例，通过扭转函数和第一Dirichlet特征函数。在等腰直角三角形上，这个猜想又失败了。然而，这个猜想也是有价值的，因为挠函数和本征函数的最大值出乎意料地接近在一起。这是一个开放的问题，量化这种封闭的领域和非线性。
英文摘要：
Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick found certain evidence for this surprising conjecture. We construct counterexamples on the half-disk, by working with the torsion function and first Dirichlet eigenfunction. On an isosceles right triangle the conjecture fails again. Yet the conjecture has merit, since the maxima of the torsion function and eigenfunction are unexpectedly close together. It is an open problem to quantify this closeness in terms of the domain and the nonlinearity.
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