Partial regularity for manifold constrained p(x)-harmonic maps

Regularity for n-Harmonic Maps

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Regularity of Harmonic Maps

Optimal Regularity of Harmonic Maps from a Riemannian Manifold into a Static Lorentzian Manifold

positive function. In such a case, we write N = N0 ×β R. In this paper we consider the case where N0 is compact. We may assume, by Nash-Moser theorem, N0 is a submanifold of R for some k > 1. By the compactness of N0, there exist constants βmin, βmax > 0 such that βmin ≤ β(x) ≤ βmax for all x ∈ N0. Let M be a Riemannian manifold with non-empty boundary ∂M . For a map w = (u, t) : M → N0 ×β R, w...

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...

Existence and Partial Regularity Results for the Heat Flow for Harmonic Maps