3-Commutators Estimates and the Regularity of 1/2-Harmonic Maps into Spheres
نویسندگان
چکیده
We prove the regularity of weak 1/2−harmonic maps from the real line into a sphere. The key point in our result is first a formulation of the 1/2−harmonic map equation in the form of a non-local linear Schrödinger type equation with a 3-terms commutators in the right-hand-side . We then establish a sharp estimate for these 3-commutators.
منابع مشابه
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,...
متن کاملRegularity of the Space of Harmonic 2-spheres in the Unit 4-sphere
A harmonic map of the Riemann sphere into the unit 4-dimensional sphere has area 4πd for some positive integer d, and it is well-known that the space of such maps may be given the structure of a complex algebraic variety of dimension 2d+4. When d less than or equal to 2, the subspace consisting of those maps which are linearly full is empty. The twistor fibration from complex projective 3-space...
متن کاملRegularity Properties of Commutators and Layer Potentials Associated to the Heat Equation
In recent years there has been renewed interest in the solution of parabolic boundary value problems by the method of layer potentials. In this paper we consider graph domains D = {{x, t): x > /(/)} in SH , where the boundary function / is in /, ,2(BMO). This class of domains would appear to be the minimal smoothness class for the solvability of the Dirichlet problem for the heat equation by th...
متن کاملA Regularity Theory of Biharmonic Maps
In this article we prove the regularity of weakly biharmonic maps of domains in Euclidean four space into spheres, as well as the corresponding partial regularity result of stationary biharmonic maps of higher-dimensional domains into spheres. c © 1999 John Wiley & Sons, Inc. Introduction In this article we consider the notion of biharmonic maps and begin an analytic study of the regularity pro...
متن کاملRegularity 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...
متن کامل