Fourth order differential operators with interior degeneracy and generalized Wentzell boundary conditions

2022/07/16 by Camasta, Alessandro, Fragnelli, Genni
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2207.07959

Abstract

In this paper we consider the fourth order operators A1u := (au")" and A2u := au"" in divergence form and non divergence form, respectively, where a, defined in [0, 1] with values in R+, degenerates in an interior point of the interval. Using the semigroup technique, under suitable assumptions on a, we study the generation property of these operators associated to generalized Wentzell boundary conditions, proving the well posedness of the corresponding parabolic problems.

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• Elliptic fourth-order operators with Wentzell boundary conditions on Lipschitz domains
• A degenerate operator in non divergence form
• Interior degenerate/singular parabolic equations in nondivergence form: well-posedness and Carleman estimates
• Singular parabolic operators in the half-space with boundary degeneracy: Dirichlet and oblique derivative boundary conditions