# 복소평면에서 일반화된 코시-리만 방정식의 해의 존재성 (On the solutions of the Cauchy-Riemann equation in complex plane)

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복소평면에서 일반화된 코시-리만 방정식의 해의 존재성 (On the solutions of the Cauchy-Riemann equation in complex plane) | |
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제안자 | |

자문교원 | 안흥주 |

연도 | 2017 |

타입 | A형 과제 |

코스 | 프란시스 크릭 |

매칭여부 | |

참여학생수 | |

소개동영상 |

### 제안 배경

### 과제 목표

The aim of this research is to study the property of solutions in the diverse functions spaces of the Cauchy-Riemnn equation on the whole complex plane or unbounded domains

### 과제 내용

- To understand the critical importance of the Cauchy-Riemann equation in complex plane or a domain. We study how to approach the function theory of complex variable using the Cauchy-Riemann equation.
- Complex differentiability, real differentiability, conformal mapping, and analyticity
- How to solve the non-homogeneous Cauchy-Riemann equation: integral representation and L^2 Hoermander method
- To study function spaces defined on the whole complex plane or unbounded domains
- Physical interpretation and potential theory

### 참고자료

References 1) B. Shokirov, On the solutions of generalized Cauchy–Riemann system, Complex Variables and Elliptic Equations, 59(8):1118-1130, 2014

2) Heungju Ahn. Global boundary regularity for the -equation on q-pseudoconvex domains. Math. Nachr., 280(4):343–350, 2007