Revisiting the C1,αh-principle for the Monge–Ampère equation

The Dirichlet Problem of Hessian Equation in Exterior Domains

“…In this case, the concept of distributional σ 2 was introduced by Iwaniec [21] in the name of weak Hessian. Lewicka and Pakzad [26] (see also [13,10]) noticed that (1.1) is closely related to isometric immersion of surfaces into R 3 . Using the convex integration method there, they showed that C 1,α ( Ω) very weak solutions to (1.1) are dense in C 0 ( Ω) for any α < 1/7 and f ∈ L 7/6 (Ω).…”