### Renormalized Energy and Forces on Dislocations

Giovanni Leoni

Carnegie Mellon University

Department of Mathematical Sciences

We discuss, from a variational viewpoint, the equilibrium problem for
a finite number of Volterra dislocations in a plane domain. For a
given set of singularities at fixed locations, we characterize elastic
equilibrium as the limit of the minimizers of a family of energy
functionals, obtained by a finite-core regularization of the
elastic-energy functional. We give a sharp asymptotic estimate of the
minimum energy as the core radius tends to zero, which allows to
eliminate this internal length scale from the problem.