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arXiv · 2307.07776

Global solvability of the Laplace equation in weighted Sobolev spaces

Bilal T. Bilalov·Natavan P. Nasibova·Lubomira G. Softova·Salvatore Tramontano
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Abstract

We consider a non-local boundary value problem for the Laplace equation in unbounded studding the weak and strong solvability of that problem in the framework of the weighted Sobolev space $W^{1,p}_ν$, with a Muckenhoupt weight. We proved that if any weak solution belongs to the space $W_ν^{2,p}$, then it is also a strong solution and satisfies the corespding boundary conditions. It should be noted that such problems do not fit into the general theory of elliptic equations and require a special technique.

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Bilal T. Bilalov, Natavan P. Nasibova, Lubomira G. Softova, Salvatore Tramontano. 2025-10-08. Global solvability of the Laplace equation in weighted Sobolev spaces. https://doi.org/10.4418/2025.80.2.5

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