Geometric PDE and Applied Analysis Seminar (August 14, 2024)

Title: Carderón-Zygmund estimates for fully nonlinear equations

Speaker: Dr. Shuhei Kitano (Waseda University)

Abstract: The Carderón—Zygmund estimate states that the \(L^p\) norm of solutions to elliptic equations can be controlled by in terms of the \(L^p\) norm for the source terms. For linear equations, it is well-known that this estimate holds for any exponents \(p>1\) but not \(p=1\). In contrast, our main result shows the estimate holds with \(p=1\) for a certain class of fully nonlinear equations.