Schwarz-type problem of nonhomogeneous Cauchy–Riemann equation on a triangle

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• 作者：Yufeng Wang^a ; ^{wh_yfwang@hotmail.com} ; Yanjin Wang^b ; ^{wang_jasonyj2002@yahoo.com}
• 关键词：Schwarz– ; Poisson formula ; Cauchy– ; Pompeiu formula ; Triangle ; Schwarz-type problem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 May 2011
• 年：2011
• 卷：377
• 期：2
• 页码：557-570
• 全文大小：207 K

文摘

We consider the Schwarz-type boundary-value problem (BVP) of the nonhomogeneous Cauchy–Riemann equation on an isosceles orthogonal triangle. By the technique of plane parqueting and the Cauchy–Pompeiu formula on the triangle, the Schwarz–Poisson formula is obtained. We also investigate boundary behaviors of the Schwarz-type operator and the Pompeiu-type operator. Especially, boundary-values at the corners are proved to exist. Finally, the solution of the Schwarz-type BVP is explicitly obtained.