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 $(1,\infty )$ for any real accretive (nonsymmetric) matrix $A$ of coefficients.

10 pages