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February 21, 2026Differential Equations

On the Boundary Value Problem for a GeneralizedCauchy–Riemann Equation in Lens and Lune

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Authors

ADA. DaryaNTN. Taghizadeh

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Overview

Analysis investigates boundary behavior of operators in lens domain, highlighting solution mechanisms.

Key Points

  • This research aims to address the Schwarz boundary value problem for a generalized Cauchy–Riemann equation.
  • Applied the parqueting-reflection principle to obtain a covering for the complex plane.
  • Introduced T-type and poly-Schwarz operators to study their properties.
  • Examined the boundary behavior of the operators in the lens domain.
  • Provided an explicit solution to the Schwarz problem for the inhomogeneous generalized Cauchy–Riemann equation.
  • Demonstrated the effectiveness of the newly defined operators in solving complex differential equations.

Cite This Study

Darya et al. (2025) studied this question.

synapsesocial.com/papers/69994a7f873532290d01ee5ahttps://doi.org/10.1134/s0012266125100088
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1On the Solvability of Schwarz Problems for the Inhomogeneous Cauchy–Riemann and Polyanalytic Equations2026
  2. 2Schwarz Problem for Model Partial Differential Equations with One Complex Variable2024 · 3 citations
  3. 3The Riemann Boundary Value Problem in a Half-Plane for Generalized Analytic Functions with a Supersingular Line2026
  4. 4Bicomplex Hardy Classes of Solutions to Beltrami Equations and the Schwarz Boundary Value Problem2026
  5. 5Cauchy Problem for Hyperbolic Equations with Nonlocal Potential-Type Terms: Series Expansions of Solutions2026