Gradient potential estimates
Pointwise gradient bounds via Riesz potentials like those available for the Poisson equation actually hold for general quasilinear equations.
Gradient theory for plasticity via homogenization of discrete dislocations
We deduce a macroscopic strain gradient theory for plasticity from a model of discrete dislocations. We restrict our analysis to the case of a cylindrical symmetry for the crystal under study, so that the mathematical formulation will involve a two-dimensional variational problem. The dislocations are introduced as point topological defects of the strain fields, for which we compute the elastic energy stored outside the so-called core region. We show that the -limit of this energy (suitably rescaled),...
Green's functions for elliptic and parabolic equations with random coefficients.
Group Actions on the Solutions of Linear Partial Differential Equations.