Regularity of p-harmonic maps from the p-dimensional ball into a sphere.
Stationary p-harmonic maps into spheres
Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions
We prove that minimizers of the functional , ⊂ , n ≥ 3, which satisfy the Dirichlet boundary condition on for g: → with zero topological degree, converge in and for any α<1 - upon passing to a subsequence - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.
On the differentiability of solutions of quasilinear elliptic equations
Weak compactness of solutions for fourth order elliptic systems with critical growth
We consider a class of fourth order elliptic systems which include the Euler-Lagrange equations of biharmonic mappings in dimension 4 and we prove that a weak limit of weak solutions to such systems is again a weak solution to a limit system.
On polyharmonic maps into spheres in the critical dimension
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