The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$. The second aim is to consider the entire solutions of another PDE, which is a generalization of the well-known PDE of tubular surfaces.

中文翻译：

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eikonal 方程和相关 PDE 的变体的完整解

本文的目的是双重的。第一个目标是描述偏微分方程 (PDE) 的整个解$u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$， 在哪里乙是一个常数并且G是多项式或整函数$\mathbb {C}^2$. 第二个目标是考虑另一个 PDE 的整个解，它是众所周知的管状表面 PDE 的推广。