Generalized Wentzell boundary conditions for second order operators with interior degeneracy
We consider operators in divergence form, A1u = (au')', and in nondivergence form, A2u = 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 A1 and A2, equipped with general Wentzell boundary conditions, are nonpositive and self-adjoint on spaces of L2type.
Discrete and Continuous Dynamical Systems - Series S
Fragnelli, G., Goldstein, G., Goldstein, J., Mininni, R., & Romanelli, S. (2016). Generalized Wentzell boundary conditions for second order operators with interior degeneracy. Discrete and Continuous Dynamical Systems - Series S, 9 (3), 697-715. https://doi.org/10.3934/dcdss.2016023