Unique continuation for fully nonlinear elliptic equations

Scott N. Armstrong, Luis Silvestre

Research output: Contribution to journalArticle

Abstract

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 C1,1. We do not assume that the nonlinearity is convex or concave, and thus a priori C2 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 which it is assumed to vanish. This then permits us to conclude with an application of a classical unique continuation result for linear equations.

Original languageEnglish (US)
Pages (from-to)921-926
Number of pages6
JournalMathematical Research Letters
Volume18
Issue number5
DOIs
StatePublished - Sep 2011

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ASJC Scopus subject areas

  • Mathematics(all)

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