The dimensional estimates of exponential growth solutions to uniformly elliptic equations of non-divergence form

Abstract

<p style='text-indent:20px;'>In this paper, we demonstrate that, for general second order uniformly elliptic equations of non-divergence form in unbounded cylinders with zero boundary condition, the space of solutions with a given exponential growth is of finite dimension. In particular, we generalize a result of Hang and Lin (1999) [<xref ref-type="bibr" rid="b4">4</xref>] in the non-divergence's setting by using a different approach. This allows us to consider the general lower order terms. Furthermore, a sharp estimate of the dimension is established by using the mean value inequality.</p>