The analytic continuation of solutions to elliptic boundary value problems in two independent variables

DOI10.1016/0022-247X(80)90045-1zbMath0447.35016MaRDI QIDQ1146315

Robert F. Millar

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

singularitiesanalytic continuationelliptic boundary value problemselliptic Cauchy problemHelmholtz's equationsLaplace's equations

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Integral representations of solutions to PDEs (35C15) Analyticity in context of PDEs (35A20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Continuation and prolongation of solutions to PDEs (35B60)

Related Items

Eigenvalues and eigenfunctions of double layer potentials ⋮ Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains ⋮ On convergence and inherent oscillations within computational methods employing fictitious sources ⋮ On analytic continuability of the missing Cauchy datum for Helmholtz boundary problems ⋮ On the representation of two-dimensional scalar wave fields in the complex plane ⋮ From reflections to a uniform elliptic growth ⋮ Series expansions of solutions of plane elliptic partial differential equations in domains of arbitrary shape ⋮ The analytic continuation of solutions of the generalized axially symmetric Helmholtz equation ⋮ The Cauchy problem for an axially symmetric equation and the Schwarz potential conjecture for the torus ⋮ Hele–Shaw flows with a free boundary produced by multipoles

Cites Work

• A survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficients
• The Dirichlet problem for the Helmholtz equation
• On the reflection laws of second order differential equations in two independent variables
• Singularities of solutions to linear, second order analytic elliptic equations in two independent variables I. The completely regular boundary
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