Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Table of Contents - 2000 - Volume 130, Issue 04  

Research Article

Quantitative continuation from a measurable set of solutions of elliptic equations

S. Vessellaa1

a1 DIMAD, via Lombroso 6/17-50134, Firenze, Italy

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 xs2208 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.

(Received October 19 1998)

(Accepted May 20 1999)