Well-posedness of a mixed boundary value problem for the multidimensional Laplace equation
DOI:
https://doi.org/10.70474/fky72m80Keywords:
well-posedness, mixed boundary value problem, multidimensional Laplace equation, spherical functions, Bessel functionAbstract
Mixed boundary value problems for multidimensional hyperbolic equations in generalized spaces have been well studied. In the author’s works, it has been proved that this problem admits a unique classical solution. However, mixed boundary value problems for multidimensional elliptic equations have not been investigated. In this paper, unique solvability is established and an explicit form of the classical solution is obtained for the mixed boundary value problem in a cylindrical domain for the multidimensional Laplace equation.
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