Unique continuation for fully nonlinear elliptic equations

Scott 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 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 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
StatePublished - Sep 2011

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Fully Nonlinear Elliptic Equations
Unique Continuation
Vanish
Harnack Inequality
Viscosity Solutions
Open set
Linear equation
Regularity
Nonlinearity
Oscillation
Zero
Estimate

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Armstrong, S., & Silvestre, L. (2011). Unique continuation for fully nonlinear elliptic equations. Mathematical Research Letters, 18(5), 921-926.

Unique continuation for fully nonlinear elliptic equations. / Armstrong, Scott; Silvestre, Luis.

In: Mathematical Research Letters, Vol. 18, No. 5, 09.2011, p. 921-926.

Research output: Contribution to journalArticle

Armstrong, S & Silvestre, L 2011, 'Unique continuation for fully nonlinear elliptic equations', Mathematical Research Letters, vol. 18, no. 5, pp. 921-926.
Armstrong, Scott ; Silvestre, Luis. / Unique continuation for fully nonlinear elliptic equations. In: Mathematical Research Letters. 2011 ; Vol. 18, No. 5. pp. 921-926.
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