Uniqueness of Energy Minimizing Maps for Almost All Smooth Boundary Data
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چکیده
A b stra c t. Here for a smooth bounded Euclidean domain-and a smooth Riemannian manifold N , we show that almost every smooth map ' : @-! N serves as boundary data for at most one energy minimizing map u :-! N [Theorem 5. 2]. We also obtain some uniform boundary regularity estimates for energy minimizers [Theorem 2. 1 ], which n ot only are important to our proof, but also imply some other properties of energy minimizers [Corollaries 2. 6{2.9] .
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Uniqueness of Energy Minimizing Maps for Almost All Smooth Boundary Data
Here for a smooth bounded Euclidean domain Ω and a smooth Riemannian manifold N , we show that almost every smooth map φ : ∂Ω→ N serves as boundary data for at most one energy minimizing map u : Ω→ N [Theorem 5.2]. We also obtain some uniform boundary regularity estimates for energy minimizers [Theorem 2.1], which not only are important to our proof, but also imply some other properties of ener...
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