Characterization of the weighted Sobolev space $H_{\beta}^{s}(\Omega)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients

V. J. Ervin

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arXiv · 2404.04658

Characterization of the weighted Sobolev space $H_{\beta}^{s}(\Omega)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients

V. J. Ervin

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Abstract

In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in $\mathbb{R}^{2}$, we establish a characterization of the weighted Sobolev space $H_{\beta}^{s}(\Omega)$ in terms of the decay rate of Fourier-Jacobi coefficients. This framework is then used to give a precise analysis of the solution to the fractional Laplace equation on the unit disk.

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V. J. Ervin. 2024-04-06. Characterization of the weighted Sobolev space $H_{\beta}^{s}(\Omega)$ in $\mathbb{R}^{2}$ in terms of the decay rate of Fourier-Jacobi coefficients. https://arxiv.org/abs/2404.04658

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