Some contributions to geometric variational problems involving nonlocal energies

∗ In multiply connected domains, critical points do exist for small ε (Berlyad, Rybalko 10 for doubly connected domain, Dos Santos 09 for general multiply connected domains).. ∗

The proof of regularity in dimension 2m uses estimates by Riesz potentials and Sobolev inequalities; it can be generalized to a wide class of nonlinear elliptic systems of order 2m..

Under the restriction 2 m 4, we prove the full Hölder regularity of weakly harmonic maps (i.e., weak solutions of its Euler–Lagrange equation) from M to N in the case that the

stationary minimal surfaces in a higher dimensional manifold we may as well consider the situation where the supporting submanifold has

Wood [13], Karcher and Wood [8] established constancy results for smooth harmonic maps from an n-dimensional bounded, star-shaped domain (into.. a general target

(The main problem without such a hypothesis would be to prove the meromorphic extension of the map f near any non- minimal point.) On the other hand, the assumption that M be

Fractional harmonic maps and weighted harmonic maps with free boundary In this section, our goal is to review in details the notion of weakly s-harmonic maps, the

Patrick Courilleau, Serge Dumont, Rejeb Hadiji. Regularity of minimizing maps with values in S 2 and some numerical simulations.. In order to minimize the energy, we ha ve followed