Bilinear embedding for real elliptic differential operators in divergence form with potentials

Abstract

We present a simple Bellman function proof of a bilinear estimate for elliptic operators in divergence form with real coefficients and with nonnegative potentials. The constants are dimension-free. The p-range of applicability of this estimate is ( 1 , ∞ ) for any real accretive (nonsymmetric) matrix A of coefficients.