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- W4297083073 abstract "Let $Omega$ be a smooth bounded simply connected domain in $mathbb{R}^2$. We investigate the existence of critical points of the energy $E_varepsilon (u)=1/2int_Omega |nabla u|^2+1/(4varepsilon^2)int_Omega (1-|u|^2)^2$, where the complex map $u$ has modulus one and prescribed degree $d$ on the boundary. Under suitable nondegeneracy assumptions on $Omega$, we prove existence of critical points for small $varepsilon$. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disc. Next, we prove that critical points exist in most of the domains." @default.
- W4297083073 created "2022-09-26" @default.
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- W4297083073 date "2013-02-22" @default.
- W4297083073 modified "2023-10-18" @default.
- W4297083073 title "Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains" @default.
- W4297083073 doi "https://doi.org/10.48550/arxiv.1302.5546" @default.
- W4297083073 hasPublicationYear "2013" @default.
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