In this paper we study the boundary value problem for the equation div (D(del u)del div (div(vertical bar del u vertical bar(p-2)del u + beta del u/vertical bar del u vertical bar))) + au = f in the z = (x, y) plane. This problem is derived from a continuum model for the relaxation of a crystal surface below the roughing temperature. The mathematical challenge is of twofolds. First, the mobility D(del u) is a 2 x 2 matrix whose smallest eigenvalue is not bounded away from 0 below. Second, the equation contains the 1-Laplace operator, whose mathematical properties are still not well-understood. Existence of a weak solution is obtained. In particular, vertical bar del u vertical bar is shown to be bounded when p > 4/3.
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机译：在本文中，我们研究了方程式的边值问题（D（del U）del div（div（垂直bar delu垂直栏（p-2）del u + beta del U /垂直bar delu垂直条）） ）z =（x，y）平面中的+ au = f。 该问题来自连续型模型，用于松弛低于粗加工温度的晶体表面。 数学挑战是双重的。 首先，移动性D（Del U）是一个2×2矩阵，其最小的特征值不是偏向于下面的0。 其次，该等式包含1-laplace运算符，其数学属性仍然不受欢迎。 获得弱溶液的存在。 特别地，垂直的Bar Del U垂直条显示在P> 4/3时界定。
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