Regularity Issues for Cosserat Continua and $p$-Harmonic Maps

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...

Existence and regularity results for the gradient flow for p - harmonic maps ∗

We establish existence and regularity for a solution of the evolution problem associated to p-harmonic maps if the target manifold has a nonpositive sectional curvature.

Regularity Theorems and Energy Identities for Dirac-harmonic Maps

We study Dirac-harmonic maps from a Riemann surface to a sphere Sn. We show that a weakly Dirac-harmonic map is in fact smooth, and prove that the energy identity holds during the blow-up process.