Year: 2026
Type: article
Abstract: We prove well-posedness and higher-order regularity for a linear structurally damped plate equation with inhomogeneous Dirichlet–Neumann boundary conditions on the half-space and on bounded domains. To this end, we study maximal regularity properties of the related first-order system on weighted Sobolev spaces of arbitrarily high smoothness. In particular, we consider Sobolev spaces with power weights that measure the distance to the boundary. This allows us to avoid unnatural compatibility conditions for the data and treat the plate equation with rough inhomogeneous boundary conditions on bounded $$C^{1,\kappa }$$ C 1 , κ -domains, where $$\kappa \in (0,1)$$ κ ∈ ( 0 , 1 ) depends on the exponent of the spatial power weight, but is independent of the smoothness of the data. Our methods can serve as an example to treat more complicated mixed-order systems as well.
Source: Mathematische Annalen
Authors: Robert Denk, Floris B. Roodenburg
Institutions: University of Konstanz, Delft University of Technology
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7154587574