Global solvability of the Laplace equation in weighted Sobolev spaces

2023/07/15 by B. T. Bilalov, Bilalov, Bilal T., Natavan P. Nasibova +5
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2307.07776

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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