中斜型偏微分方程的全解 $\mathbb{C}^2$

IF 0.5 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2025-06-25 DOI:10.1007/s10476-025-00086-5

L. Yang, W. Chen, Q. Wang

引用次数: 0

摘要

本文刻画了下列直角型偏微分方程$$u^2+(a_{1}u_{z_{1}}+a_{2}u_{z_{2}})^2=p,\,\,\, u_{z_{1}}^2+(a_{0}u+a_{2}u_{z_{2}})^2=p ,$$和$$(u+a_{1}u_{z_{1}})^2+(a_{0}u+a_{2}u_{z_{2}})^2=p,$$的全部解，其中p在$\mathbb{C}^2$中是多项式，$a_{0},a_{1},a_{2}$在$\mathbb{C}$中是常数。给出了描述，并辅以各种实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Entire solutions of the eiconal type partial differential equations in $\mathbb{C}^2$

This paper characterizes the entire solutions of the following eiconal type partial differential equations

$$u^2+(a_{1}u_{z_{1}}+a_{2}u_{z_{2}})^2=p,\,\,\, u_{z_{1}}^2+(a_{0}u+a_{2}u_{z_{2}})^2=p ,$$

and

$$(u+a_{1}u_{z_{1}})^2+(a_{0}u+a_{2}u_{z_{2}})^2=p,$$

where p is a polynomial in $\mathbb{C}^2$, and $a_{0},a_{1},a_{2}$ are constants in $\mathbb{C}$. Descriptions are given and complemented by various examples.

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.

中斜型偏微分方程的全解 \(\mathbb{C}^2\)

摘要