Transmission problems for simply connected domains in the complex plane

被引：0

作者：

Carro, Maria J. ^{[1
,2
]}

Naibo, Virginia ^{[3
]}

Soria-Carro, Maria ^{[4
]}

机构：

[1] Univ Complutense Madrid, Dept Anal & Appl Math, Plaza Ciencias 3, Madrid 28040, Spain

[2] Inst Ciencias Matemat ICMAT, Madrid, Spain

[3] Kansas State Univ, Dept Math, 138 Cardwell Hall,1228 N Martin Luther King Jr Dr, Manhattan, KS 66506 USA

[4] Rutgers State Univ, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2025年 / 433卷

关键词：

Transmission problems; Graph simply connected domains; Conformal maps; Muckenhoupt weights; DIRICHLET PROBLEM; REGULARITY; SPACES;

D O I：

10.1016/j.jde.2025.113216

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study existence and uniqueness of a transmission problem in simply connected domains in the plane with data in weighted Lebesgue spaces by first investigating solvability results of a related novel problem associated to a homeomorphism in the real line and domains given by the upper and lower half planes. Our techniques are based on the use of conformal maps and Rellich identities for the Hilbert transform, and are motivated by previous works concerning the Dirichlet, Neumann and Zaremba problems. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：35

共 35 条

[1]

Ahlfors LarsV., 1966, LECT QUASICONFORMAL, V10

[2] THE BOUNDARY CORRESPONDENCE UNDER QUASICON-FORMAL MAPPINGS [J].