We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as \(g(u)|\nabla u|^q\), where \(1<q<2\) and g(s) is a continuous function. Data belong to \(L^m(\Omega )\) with \(1\le m <\frac{N}{2}\) as well as measure data instead of \(L^1\)-data, so that unbounded solutions are expected. Our aim is, given \(1\le m<\frac{N}{2}\) and \(1<q<2\), to find the suitable behaviour of g close to infinity which leads to existence for our problem. We show that the presence of g has a regularizing effect in the existence and summability of the solution. Moreover, our results adjust with continuity with known results when either g(s) is constant or \(q=2\).

我们考虑由具有不连续系数并具有次二次梯度项的线性算子驱动的椭圆方程的齐次Dirichlet问题。此梯度项的行为为\（g（u）| \ nabla u | ^ q \），其中\（1 <q <2 \）和g（s）是连续函数。数据属于\（L ^ m（\ Omega）\）和\（1 \ le m <\ frac {N} {2} \），并且属于测量数据而不是\（L ^ 1 \）- data，因此无限解决方案是可以预期的。我们的目标是，给定\（1 \ le m <\ frac {N} {2} \）和\（1 <q <2 \），找到g的合适行为接近无限，导致存在我们的问题。我们证明g的存在对解决方案的存在和可加性具有正则化作用。此外，当g（s）恒定或\（q = 2 \）时，我们的结果将与已知结果连续地调整。