Existence of Innnitely Many Weakly Harmonic Extensions into S 2 for Non-constant Boundary Maps
نویسنده
چکیده
We prove the existence of innnitely many weakly harmonic maps from a domain of R n into S 2 for non-constant smooth boundary data.
منابع مشابه
Harmonic and Quasi-harmonic Spheres, Part Iii Rectiiablity of the Parabolic Defect Measure and Generalized Varifold Flows
This is the third part of our project initiated in LW1] on the study of the weakly convergent sequence of smooth (or certain classes of weak) solutions to the heat equation of harmonic maps or approximated harmonic maps (i.e. the negative gradient ow of the generalized Ginzburg-Landau functionals). The general situation for the heat ow of harmonic maps is as follows. Let u n (x; t) : M R + ! N ...
متن کاملBoundary 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 کاملUniversit at Konstanz Weakly Hyberbolic Equations in Domains with Boundaries Weakly Hyperbolic Equations in Domains with Boundaries
We consider weakly hyperbolic equations of the type u tt (t)+a(t)Au(t) = f(t; u(t)), u(0) = u 0 , u t (0) = u 1 ,u(t) 2 D(A), t 2 0; T], for a function u : 0; T] ?! H, T 2 0; 1], H a separable Hilbert space, A being a non-negative, self-adjoint operator with domain D(A). The real function a is assumed to be non-negative, continuous and (piecewise) continuous diierentiable, and the derivative a ...
متن کاملHarmonic tori in spheres and complex projective spaces
Introduction A map : M ! N of Riemannian manifolds is harmonic if it extremises the energy functional: Z jdj 2 dvol on every compact subdomain of M. Harmonic maps arise in many diierent contexts in Geometry and Physics (for an overview, see 15,16]) but the setting of concern to us is the following: take M to be 2-dimensional and N to be a Riemannian symmetric space of compact type. In this case...
متن کاملHarmonic and Quasi-Harmonic Spheres, Part III Recti ablity of the Parabolic Defect Measure and Generalized Varifold Flows
This is the third part of our project initiated in [LW1] on the study of the weakly convergent sequence of smooth (or certain classes of weak) solutions to the heat equation of harmonic maps or approximated harmonic maps (i.e. the negative gradient ow of the generalized Ginzburg-Landau functionals). The general situation for the heat ow of harmonic maps is as follows. Let un(x; t) : M R+ ! N be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007