Regularity Bootstrapping for 4th-order Nonlinear Elliptic Equations

Abstract

satisfies (1.4) b(Du(x))ξijξkl ≥ Λ1 ‖ξ‖ 2 . Our main result is the following: Suppose that conditions (1.1) and (1.4) are met on some open set U ⊆ S (space of symmetric matrices). If u is a C solution with Du(B1) ⊂ U , then u is smooth on the interior of the domain B1. One example of such an equation is the Hamiltonian Stationary Lagrangian equation, which governs Lagrangian surfaces that minimize the area functional