It is well known that for higher order elliptic equations, the positivity preserving property (PPP) may fail. In striking contrast to what happens under Dirichlet boundary conditions, we prove that the PPP holds for the biharmonic operator on rectangular domains under partially hinged boundary conditions, i.e., nonnegative loads yield positive solutions. The result follows by fine estimates of the Fourier expansion of the corresponding Green function.

中文翻译：

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部分铰接边界条件下双调和算子的保正性质结果

众所周知，对于高阶椭圆方程，正性保持性（PPP）可能会失效。与 Dirichlet 边界条件下发生的情况形成鲜明对比，我们证明了 PPP 在部分铰接边界条件下对矩形域上的双调和算子成立，即非负载荷产生正解。结果是对相应格林函数的傅立叶展开的精细估计。