*Published Paper*

**Inserted:** 11 dec 2002

**Last Updated:** 13 dec 2002

**Journal:** Non Linear Analysis

**Volume:** 49

**Pages:** 747-755

**Year:** 2002

**Abstract:**

We consider an elliptic equation on $R^n$ of the form $\lambda \varphi-\frac{1}{2}\;\Delta \varphi +\langle DU,D\varphi\rangle=f$ with the potential $U$ regular but unbounded. We prove a maximal regularity result in the space $L^p(R^n, \nu)$ where $\nu$ is an invariant measure.

**Keywords:**
Elliptic equations, unbounded coefficients, maximal regularity, invariant measures

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