We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.

中文翻译：

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度量空间上带有反应项的Neumann p -Laplacian问题

我们使用变分方法来研究Neumann p- Laplacian问题的解的存在性和正则性，其中度量空间上的反应项具有加倍测度并支持Poincaré不等式。具有变分的函数的迹定理被应用到变分函数的定义中，并且最小化证明满足De Giorgi型条件。