We consider a class of Dirichlet boundary problems for nonlinear degenerate elliptic equations with lower order terms. We prove, using symmetrization techniques, pointwise estimates for the rearrangement of the gradient of a solution u and integral estimates. As consequence, we get apriori estimates which show how the summability of the gradient of a solution increases when the summability of the datum increases, also taking into account the presence of a zero order term which can have a regularizing effect.

中文翻译：

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具有低阶项的非线性退化椭圆型方程解的估计

我们考虑一类具有低阶项的非线性退化椭圆型方程的Dirichlet边界问题。我们使用对称化技术证明了点u估计用于解u和积分估计的梯度重排。结果，我们得到先验估计，该估计表明，当基准的可加性增加时，解决方案的梯度的可加性如何增加，同时还考虑了可能具有正则化效果的零阶项的存在。