Abstract
We study the classical Dirichlet problem in the disc with the weighted uniform norm for the weight function \({w(x) = v(x)\prod_{j=1}^s|\sin(\frac{x-x_j}{2})|^{\lambda_j}}\) , \({\{\lambda_{j}\}_{j=1}^{s}}\) are positive numbers and v is a strictly positive continuous function on the circle. Remarkably the problem has solution if and only if none of the numbers \({\{\lambda_{j}\}_{j=1}^{s}}\) is natural.
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Horváth, Á.P., Kazarian, K.S. The Dirichlet problem in weighted norm. Acta Math. Hungar. 153, 34–56 (2017). https://doi.org/10.1007/s10474-017-0749-8
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DOI: https://doi.org/10.1007/s10474-017-0749-8
Key words and phrases
- Dirichlet problem
- harmonic function
- weighted uniform convergence
- modified Poisson kernel
- weight function with zeros