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We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open subsets of ▫${\mathbb R}^d$▫.

We prove a dimension-free ▫$L^p(\Omega)\times L^q(\Omega)\times L^r(\Omega)\rightarrow L^1(\Omega\times (0,\infty))$▫ embedding for triples of elliptic operators in divergence form with complex coefficients and subject to mixed boundary conditions on ▫$\Omega$▫, and for triples of exponents ▫$p,q,r ...