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Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theoremfor a class of non symmetric second order linear elliptic operators on a convexdomain in euclidean space. The class of operators includes the Bakry-Emerylaplacian with potential and any operator with second order term the laplacianwhose first order terms have coefficients with compact support in the opendomain. The eigenvalue gap is bounded below by the gap of an associatedSturm-Liouville problem on a closed interval.

Eigenvalue gap theorems for a class of non symmetric elliptic operators on convex domains