On the regularity of weak subelliptic $F$-harmonic maps

Subelliptic Harmonic Maps

We study a nonlinear harmonic map type system of subelliptic PDE. In particular, we solve the Dirichlet problem with image contained in a convex ball.

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 for n-Harmonic Maps

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ON THE REGULARITY OF SUBELLIPTIC p-HARMONIC FUNCTIONS IN CARNOT GROUPS

In this paper we prove second order horizontal differentiability and C1,α regularity results for subelliptic p-harmonic functions in Carnot groups for p close to 2.