Abstract: We consider the problem of minimizing the first nonzero eigenvalue of an elliptic operator with Neumann boundary conditions with respect to the distribution of two conducting materials with a prescribed area ratio in a given domain. In one dimension, we show monotone properties of the first nonzero eigenvalue with respect to various parameters and […]

Abstract: In the presentation we will discuss our research program concerning the search for the most singular behaviors possible in viscous incompressible flows. These events are characterized by extremal growth of various quantities, such as the enstrophy, which control the regularity of the solution. They are therefore intimately related to the question of possible singularity […]