Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 473-483

A NOTE ON UNIQUE CONTINUATION FOR SOLUTIONS OF THE $\infty$-MEAN VALUE PROPERTY

José G. Llorente

Universitat Autňnoma de Barcelona, Departament de Matemŕtiques
08193 Bellaterra, Barcelona, Spain; jgllorente 'at' mat.uab.cat

Abstract. We consider continous functions in euclidean domains that are solutions of a nonlinear mean value property related to the infinity laplacian. It is proved that such functions must satisfy a restricted unique continuation principle in the sense that if they vanish on a ball, they must vanish on the whole domain.

2010 Mathematics Subject Classification: Primary 31C05, 35B60, 31C45.

Key words: Mean value property, infinity laplacian, unique continuation.

Reference to this article: J.G. Llorente: A note on unique continuation for solutions of the $\infty$-mean value property. Ann. Acad. Sci. Fenn. Math. 39 (2014), 473-483.

Full document as PDF file

doi:10.5186/aasfm.2014.3914