Hyperbolic Formulas in Elliptic Cauchy Problems

2010/03/18 by Dmitry P. Fedchenko, D. Fedchenko, Fedchenko, D. +3
Engineering · Mathematics · Physics and Astronomy · #35J25 (Primary) #35L15 (Secondary) #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics and Engineering Research Articles #Stability and Controllability of Differential Equations #math-ph #math.MP #msc:35J25 #msc:35L15

paper · pdf · doi:10.48550/arxiv.1003.3606

16 pages, 4 figures

arxiv created 2010/03/18 · openalex publication_date 2010/03/18 · arxiv updated 2010/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Cauchy problem for the Laplace equation in a cylindrical domain with data on a part of it's boundary which is a cross-section of the cylinder. On reducing the problem to the Cauchy problem for the wave equation in a complex domain and using hyperbolic theory we obtain explicit formulas for the solution, thus developing the classical approach of Hans Lewy (1927).

Citations

• Asymptotic solutions of oscillatory initial value problems

Related

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• Hyperbolic Cauchy problem and Leray's residue formula
• Introduction to inverse problems for hyperbolic PDEs
• On the Cauchy problem for the wave equation with data on the boundary
• The linear hyperbolic initial and boundary value problems in a domain with corners