Event Series
Event Type
Seminar
Friday, February 7, 2020 2:00 PM
Joey Zou

The Gagliardo-Nirenberg inequality allows an interpolation of L^p-based Sobolev spaces by combining L^p estimates of higher-order derivatives for p small and L^p estimates of lower-order derivatives for p large to give an L^p estimate of intermediate derivatives for p intermediate. Such estimates are useful in the study of nonlinear PDE. I will prove a more general version of the Gagliardo-Nirenberg inequality where we consider functions satisfying iterated regularity with respect to certain collections of vector fields (e.g. vector fields tangent to certain submanifolds). I will then discuss a paper by Melrose and Ritter (containing the above general proof) which applies the result to study semilinear wave equations, in particular analyzing the interaction of multiple plane waves and whether such interaction produces additional singularities compared to the linear case.