Convexity estimates for nonlinear elliptic equations and application to free boundary problems

Keywords: Littlewood-Paley estimate, functional calculus, boundary value prob- lems, second order elliptic equations and systems, square root

The quote is “A frame of s points in space requires in general 3s − 6 connecting lines to render it stiff.” For a two-dimensional pin-jointed structure, Maxwell’s statement would

It is also very useful when we make a systematic analysis of the gradients of solutions of nonlinear elliptic and parabolic problems near the boundary of the irregular domain which

Roughly speaking, his result says that at the first singular time of the mean curvature flow, the product of the mean curvature and the norm of the second fundamental form blows

Then we give at a formal level the extension of the system (1.8)–(1.9) to dimensions higher than 2. The estimate for the gradient is unchanged but the one on the curvature is

FUCHS, A general existence theorem for integral currents with prescribed mean curvature form, in Boll. FEDERGER, The singular set of area minimizing rectifiable

KOREVAAR, An Easy Proof of the Interior Gradient Bound for Solutions to the Prescribed Mean Curvature Equation, Proc. URAL’TSEVA, Local Estimates for Gradients

Andrews shows that convex surfaces moving by Gauss curvature converge to round points without any initial pinching condition.. For general speeds of higher