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)
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

희망학생