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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 2, Pages 217–223
DOI: https://doi.org/10.31857/S0044466921010038 (Mi zvmmf11195) 		 
Partial Differential Equations

Approximation of weak solutions of the Laplace equation by harmonic polynomials

M. E. Bogovskiiab

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
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DOI: https://doi.org/10.31857/S0044466921010038
Abstract: A new proof based on F. Browder's ideology is given for the theorem on the approximation of weak solutions of the Laplace equation in a bounded domain $\Omega\subset\mathbb{R}^n$, $n\ge2$, with a connected Lipschitz boundary by harmonic polynomials in the Lebesgue space $L_p(\Omega)$ and the Sobolev space $W_p^1(\Omega)$.
Key words: approximation problem, harmonic polynomials, bounded domain in $\mathbb{R}^n$, Lipschitz boundary, Lebesgue space $L_p(\Omega)$, Sobolev space $W_p^1(\Omega)$, weak solutions of the Laplace equation.
Received: 16.06.2020
Revised: 21.07.2020
Accepted: 15.08.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 2, Pages 205–211
DOI: https://doi.org/10.1134/S0965542521010036
Bibliographic databases:
Document Type: Article
UDC: 517.951
Language: Russian
Citation: M. E. Bogovskii, “Approximation of weak solutions of the Laplace equation by harmonic polynomials”, Zh. Vychisl. Mat. Mat. Fiz., 61:2 (2021), 217–223; Comput. Math. Math. Phys., 61:2 (2021), 205–211
Citation in format AMSBIB
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