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The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
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V. Kokilashvili
Published/Copyright:
March 10, 2010
Abstract
We investigate the Dirichlet problem in domains with nonsmooth boundaries when a boundary function belongs to functional classes of the Zygmund class type. A complete picture of solvability is established also in the case of existence of solutions for which explicit expressions are found.
Received: 2003-02-24
Published Online: 2010-03-10
Published in Print: 2003-September
© Heldermann Verlag
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Keywords for this article
harmonic function;
Zygmund class;
Dirichlet problem;
non-smooth boundaries
Articles in the same Issue
- On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems
- On the Mathematical Basis of the Linear Sampling Method
- Solvability and Asymptotics of Solutions of Crack-Type Boundary-Contact Problems of the Couple-Stress Elasticity
- Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data
- Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions
- About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations
- The Superstability of the Generalized D'alembert Functional Equation
- First Order Partial Functional Differential Equations with Unbounded Delay
- The Dirichlet Problem for Harmonic Functions with Boundary Values from Zygmund Classes
- On the Asymptotics of Solutions of Elliptic Equations in a Neighborhood of a Crack with Nonsmooth Front
- A Factorization Method for an Inverse Neumann Problem for Harmonic Vector Fields
- A Bound for Reflections Across Jordan Curves
- A Direct Method for Boundary Integral Equations on a Contour with a Peak
- On Two-Point Boundary Value Problems for Two-Dimensional Differential Systems with Singularities
