论文标题
一般$ p $面积的解决方案的存在和结构最小化表面
Existence and structure of solutions for general $P$-area minimizing surface
论文作者
论文摘要
我们研究了与功能性$ i（u）= \int_Ω（ϕ（x，d u + f） + hu）\，dx $相关的dirichlet和neumann边界问题的解决方案的存在和结构，其中$ ϕ（x，ξ）$，其他属性，包括convex and convex and同级$ 1 $ $ $ $ $。我们表明，存在一个基本的矢量字段$ n $，该字段$ n $是所有最小化器的存在和结构的特征。我们还调查了$ \ partialω$的屏障条件下的解决方案的存在。本文的结果概括并统一了有关存在最小梯度问题和$ p- $面积最小化表面的文献中的许多结果。
We study existence and structure of solutions to the Dirichlet and Neumann boundary problems associated with minimizers of the functional $I(u)=\int_Ω (ϕ(x, D u + F)+Hu) \, dx$, where $ϕ(x, ξ)$, among other properties, is convex and homogeneous of degree $1$ with respect to $ξ$. We show that there exists an underlying vector field $N$ that characterizes the existence and structure of all minimizers. We also investigate existence of solutions under the barrier condition on $\partial Ω$. The results in this paper generalize and unify many results in the literature about existence of minimizers of least gradient problems and $P-$area minimizing surfaces.
