# Bilinear embedding for Schr\"odinger-type operators with complex coefficients

## TL;DR

This paper extends the bilinear embedding theorem to Schrödinger-type operators with complex coefficients, divergence form, and nonnegative potentials, under mixed boundary conditions on arbitrary open sets.

## Contribution

It introduces a new variant of the bilinear embedding theorem applicable to complex coefficient operators with potentials and mixed boundary conditions.

## Key findings

- Proves a bilinear embedding theorem for Schrödinger-type operators with complex coefficients.
- Establishes results for operators with nonnegative locally integrable potentials.
- Handles arbitrary open subsets of  with mixed boundary conditions.

## Abstract

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 $\mathbb{R}^{d}$.