n/p-harmonic maps: Regularity for the sphere case

Regularity for n-Harmonic Maps

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Regularity of Harmonic Maps

Regularity of Dirac-harmonic maps

For any n-dimensional compact spin Riemannian manifold M with a given spin structure and a spinor bundle ΣM , and any compact Riemannian manifold N , we show an ǫ-regularity theorem for weakly Dirac-harmonic maps (φ, ψ) : M ⊗ΣM → N ⊗ φ∗TN . As a consequence, any weakly Dirac-harmonic map is proven to be smooth when n = 2. A weak convergence theorem for approximate Dirac-harmonic maps is establi...

Regularity of generalized sphere valued p - harmonic maps with small mean oscillations

We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1 loc ( , Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1, . . . , n, is smooth as soon as |∇u| ∈ L for any q > 1, and the norm of u in BMO is sufficiently small. Here, ⊂ R is open, and m, n are arbitrary. This extends various earlier results of Almeida [1], Ge [15], and R. M...

Boundary Regularity and the Dirichlet Problem for Harmonic Maps

In a previous paper [10] we developed an interior regularity theory for energy minimizing harmonic maps into Riemannian manifolds. In the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed Dirichlet boundary condition. We show that such maps are regular in a full neighborhood of the boundary, assuming appropriate regularity on the manifolds,...