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In this note, we present explicit conditions for symmetric gradient typeDirichlet forms to be recurrent. This type of Dirichlet form is typicallystrongly local and hence associated to a diffusion. We consider the onedimensional case and the multidimensional case, as well as the case withreflecting boundary conditions. Our main achievement is that the explicitresults are obtained under quite weak assumptions on the closability, henceregularity of the underlying coefficients. Especially in dimension one, where aHamza type condition is assumed, the construction of the sequence of functions$(u_n)_{n\in \N}$ in the Dirichlet space that determine recurrence works forquite general Dirichlet forms but is still explicit.

Explicit recurrence criteria for symmetric gradient type Dirichlet forms satisfying a Hamza type condition