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Quantitative continuation from a measurable set of solutions of elliptic equations

Published online by Cambridge University Press:  11 July 2007

S. Vessella
S. Vessella
Affiliation:
DIMAD, via Lombroso 6/17-50134, Firenze, Italy
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Abstract

Consider an open bounded connected set Ω in Rn and a Lebesgue measurable set E ⊂⊂ Ω of positive measure. Let u be a solution of the strictly elliptic equation Di (aij Dj u) = 0 in Ω, where aij ∈ C0, 1 (Ω̄) and {aij} is a symmetric matrix. Assume that |u| ≤ ε in E. We quantify the propagation of smallness of u in Ω.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 4 , August 2000 , pp. 909 - 923
Copyright
Copyright © Royal Society of Edinburgh 2001

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