Donatella Danielli

Dr. Danielli's research program lies at the interface of partial differential equations, calculus of variations, and geometric measure theory. More precisely, she is interested in elliptic and parabolic free boundary problems naturally arising in physics and engineering. Free boundary problems model phenomena where a conserved quantity or relation changes discontinuously across some value of the variables under consideration. The free boundary appears, for instance, as the interface between a fluid and the air, or water and ice. Dr. Danielli is interested in the study of regularity properties of the solution and of the interface in obstacle-type problems, where the distinctive feature is that the obstacle is confined to lie in a lower dimensional manifold, or the operator under consideration is of non-local nature. Another area of interest is the study of free boundary problems relevant in the theory of flame propagation.