The Riemann boundary value problem on non-rectifiable curves and related questions

DOI10.1080/17476933.2013.809574zbMath1314.30063OpenAlexW2053054896MaRDI QIDQ5419440

Boris A. Kats

Publication date: 6 June 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2013.809574

zbMATH Keywords

Cauchy integralnon-rectifiable curvesRiemann boundary value problemmetric dimensions

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Boundary value problems in the complex plane (30E25)

Related Items (27)

Local and weighted Marcinkiewicz exponents with applications ⋮ Marcinkiewicz exponents and integrals over non-rectifiable paths ⋮ New solvability criterion for jump problem ⋮ Riemann boundary-value problem for holomorphic matrices on non-rectifiable curve ⋮ Jump problem for differentiable functions with applications ⋮ Torsions and integrations ⋮ Interactions of germs with applications ⋮ Dirichlet spaces of domains bounded by quasicircles ⋮ Integration over nonrectifiable curves as a distribution ⋮ The jump problem for the critical Besov space ⋮ Analysis on quasidisks: a unified approach through transmission and jump problems ⋮ Plemelj-Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operators ⋮ Riemann boundary value problem on periodic non-rectifiable curve ⋮ Application of Faber polynomials to the approximate solution of the Riemann problem ⋮ Noether property and approximate solution of the Riemann boundary value problem on closed curves ⋮ Jump boundary-value problem on a contour with elongate singularities ⋮ Marcinkiewicz exponents and jump problem for Beltrami equation ⋮ Singular integral equations on non-smooth curves in Hölder-Frechét space ⋮ On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation ⋮ Integration over nonrectifiable paths with applications ⋮ Zigzags and spirals in boundary-value problems ⋮ What's new on integration over non-rectifiable curves: spirals and kernels ⋮ Doubly periodic Riemann boundary value problem for non-rectifiable curves ⋮ Well-posedness of jump problem on non-rectifiable curves ⋮ Non-rectifiable Riemann boundary value problem for bi-analytic functions ⋮ Riemann boundary value problem on non-rectifiable curves with torsion points ⋮ A jump problem on a contour with limit continuum

Cites Work

• Unnamed Item
• The Cauchy transform of certain distributions with application
• Integration over non-rectifiable curves and Riemann boundary value problems
• On solvability of the jump problem
• Hyperanalytic Riemann boundary value problem on \(d\)-summable closed curves
• Analytic functions satisfying Hölder conditions on the boundary
• The Gauss-Green theorem for fractal boundaries
• Approximate dimension applied to criteria for monogenicity on fractal domains
• Boundary value problems for quaternionic monogenic functions on non-smooth surfaces
• Hermitian decomposition of continuous functions on a fractal surface
• Riemann boundary value problem for hyperanalytic functions
• Minkowski dimension and Cauchy transform in Clifford analysis
• Surface integrals for domains with fractal boundaries and some applications to elasticity
• A note about Riemann boundary value problems on non-rectifiable curves

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