Regularity for 1/2-Harmonic Maps into Manifolds-the Critical Case
نویسنده
چکیده
In this paper we give the definition of 1/2-harmonic maps u : D → N , where D is an open set of IR and N is a k dimensional submanifold N of IRm as critical points of the functional ∫ Ω |∆ 1/4u|2dx . We write the Euler-Lagrange equation satisfied in a weak sense by the 1/2-harmonic maps, which is a nonlocal partial differential equation involving the 1/2-Laplacian operator . We prove the local Hölder continuity of solutions in H1/2(IR,N ) to a class of nonlocal equations involving the 1/2-Laplacian operator and that includes the case of 1/2-harmonic maps. The key point in our result is the reduction to a linear Schrödinger type equation with a commutator estimate of the right hand side of the equation.
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