Caltech/UCLA Joint Analysis Seminar

Abstract: Many equations of Boltzmann type have the structure of a parabolic equation with a quadratic nonlinearity, except the coefficients are nonlocal equations of the function itself. We note such equations behave a lot like singular Schrödinger operators whose potentials lie in a critical Morrey space, proving new regularization estimates for the spatially homogeneous Landau equation with moderately soft potentials. The main tools are integral inequalities with Ap weights and iterations in the style of De Giorgi-Nash-Moser theory. Joint work with Maria Gualdani.