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As ((-Delta)^{1/2}) is nonlocal and nonlinear, we realize problem (1.1) through a local problem in one more dimension by a Dirichlet to Neumann map.
In fact, we realize problem (3), through a localization method introduced by Caffarelli and Silvestre on the Euclidean space R n, through which (3) is connected to a degenerate elliptic differential equation in one dimension higher by a Dirichlet to Neumann map.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com