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# Generalized Wentzell boundary conditions for second order operators with interior degeneracy

• We consider operators in divergence form, $A_1u=(au')'$, and in nondivergence form, $A_2u=au''$, provided that the coefficient $a$ vanishes in an interior point of the space domain. Characterizing the domain of the operators, we prove that, under suitable assumptions, the operators $A_1$ and $A_2$, equipped with general Wentzell boundary conditions, are nonpositive and selfadjoint on spaces of $L^2$ type.
Mathematics Subject Classification: Primary: 47D06; Secondary: 35K65, 47B25, 47N20.

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