We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another quasilinear elliptic problem involving a parameter $p>1$ as $p\to 1^{+}$. The analysis requires estimates independent on p, as well as a precise version of the weak Euler-Lagrange equation satisfied by the solution.

中文翻译：

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平均曲率方程的 BV 解的存在性

我们证明了涉及平均曲率算子和次线性非线性的拟线性椭圆问题的有界变化解的存在。我们得到这样一个解作为另一个涉及参数的拟线性椭圆问题的解的极限$磷>1$ 作为 $磷\to 1^{+}$. 该分析需要独立于p 的估计值，以及解满足的弱 Euler-Lagrange 方程的精确版本。