We consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.

中文翻译：

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具有奇异低阶项的非矫顽拟线性椭圆算子

我们考虑一类拟线性二阶椭圆微分算子，该算子不是强制性的，而是由Marcinkiewicz空间中的函数定义的。我们证明了相应的Dirichlet问题的解决方案的存在。相关的障碍问题也得到解决。最后，当基准面更规则时，我们显示Dirichlet问题的解决方案的更高可集成性。