Unique Continuation for Fully Nonlinear Elliptic Equations

Scott N. Armstrong, Luis Silvestre
2011 Mathematical Research Letters  
We show that a viscosity solution of a uniformly elliptic, fully nonlinear equation which vanishes on an open set must be identically zero, provided that the equation is C 1,1 . We do not assume that the nonlinearity is convex or concave, and thus a priori C 2 estimates are unavailable. Nevertheless, we use the boundary Harnack inequality and a regularity result for solutions with small oscillations to prove that the solution must be smooth at an appropriate point on the boundary of the set on
more » ... dary of the set on which it is assumed to vanish. This then permits us to conclude with an application of a classical unique continuation result for linear equations.
doi:10.4310/mrl.2011.v18.n5.a9 fatcat:kjy5mw65vngj3bvbrvlalrgvs4