The skew derivative problem in the exterior of open curves in a plane

DOI10.4171/ZAA/788zbMath0888.35027OpenAlexW2085180847MaRDI QIDQ1368792

P. A. Krutitskii

Publication date: 4 June 1998

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/788

zbMATH Keywords

regularityexistenceFredholm integral equationuniqueness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Integral equations with kernels of Cauchy type (45E05) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items (10)

Application of the discrete Fourier transform to solving the Cauchy integral equation ⋮ Improved quadrature formula for a single-layer potential ⋮ Numerical method for an integral-algebraic system ⋮ Generalization of the Neumann problem to harmonic functions outside cuts on the plane ⋮ Explicit solutions of integral equations and relations for potentials ⋮ Numerical method for the solution of integral equations in a problem with directional derivative for the Laplace equation outside open curves ⋮ The harmonic problem in the plane with cuts under boundary conditions of the third kind ⋮ Boundary value problem for the Laplace equation outside cuts on the plane with different conditions of the third kind on opposite sides of the cuts ⋮ Numerical treatment of the Cauchy integral equation by discrete Fourier transform ⋮ Quadrature formula for the double layer potential with differentiable density

Cites Work

• The mixed problem for the Helmholtz equation in a multiply connected region
• Dirichlet's problem for the Helmholtz equation outside cuts in a plane
• Neumann's problem for the Helmholtz equation outside cuts in the plane
• The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
• Layer potentials and boundary value problems for the helmholtz equation in the complement of a thin obstacle
• An Existence Theorem for the Reduced Wave Equation
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