Consider an open bounded connected set Ohm in R-n and a Lebesgue measurable set E subset of subset of Ohm of positive measure. Let u be a solution of the strictly elliptic equation D-i(a(ij)D(j)u) = 0 in Omega, where a(ij) is an element of C-0,C-1(<(Omega)over bar>) and {a(ij)} is a symmetric matrix. Assume that /u/ less than or equal to epsilon in E. We quantify the propagation of smallness of u in Omega.
QUANTITATIVE CONTINUATION OF SOLUTION OF ELLIPTIC EQUATIONS FROM A MEASURABLE SET / S. VESSELLA. - In: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. - ISSN 0013-0915. - STAMPA. - 130A:(2000), pp. 909-923. [10.1017/S0308210500000494]
QUANTITATIVE CONTINUATION OF SOLUTION OF ELLIPTIC EQUATIONS FROM A MEASURABLE SET
VESSELLA, SERGIO
2000
Abstract
Consider an open bounded connected set Ohm in R-n and a Lebesgue measurable set E subset of subset of Ohm of positive measure. Let u be a solution of the strictly elliptic equation D-i(a(ij)D(j)u) = 0 in Omega, where a(ij) is an element of C-0,C-1(<(Omega)over bar>) and {a(ij)} is a symmetric matrix. Assume that /u/ less than or equal to epsilon in E. We quantify the propagation of smallness of u in Omega.
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