Let Sigma be a surface of constant mean curvature in R-3 with multiple Delaunay ends. Assuming that Sigma is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation epsilon Delta u + epsilon(-1)u(1 - u(2)) = l(epsilon) in R-3 such that as epsilon -> 0 the zero level set of u(epsilon) approaches Sigma. Moreover, on compacts of the connected components of R-3\Sigma we have 1 - vertical bar u(epsilon)vertical bar -> 0 uniformly.
Multiple Delaunay ends solutions of the Cahn-Hilliard equation
Rizzi M.
2022-01-01
Abstract
Let Sigma be a surface of constant mean curvature in R-3 with multiple Delaunay ends. Assuming that Sigma is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation epsilon Delta u + epsilon(-1)u(1 - u(2)) = l(epsilon) in R-3 such that as epsilon -> 0 the zero level set of u(epsilon) approaches Sigma. Moreover, on compacts of the connected components of R-3\Sigma we have 1 - vertical bar u(epsilon)vertical bar -> 0 uniformly.File in questo prodotto:
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