Regularity for the Harmonic-Einstein equation

Maximal Regularity of the Discrete Harmonic Oscillator Equation

We provide a geometrical interpretation for the best approximation of the discrete harmonic oscillator equation formulated in a general Banach space setting. We give a representation of the solution, and a characterization of maximal regularity-or well posednesssolely in terms of R-boundedness properties of the resolvent operator involved in the equation.

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...

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,...