4 citations · 4 across the 6 of their papers we have counts for
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The Closed Range Property and Gaffney's Inequality of the De Rham Complex in Unbounded Domains
Dirk Pauly, Marcus Waurick
The classical Poincaré estimate establishes closedness of the range of the gradient in unweighted -spaces as long as is contained in a slab, that i…
Biharmonic Equations
Dirk Pauly, Alberto Valli
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of partic…
Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron
We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed bou…
A Compactness Result for the div-curl System with Inhomogeneous Mixed Boundary Conditions for Bounded Lipschitz Domains and Some Applications
Dirk Pauly, Nathanael Skrepek
For a bounded Lipschitz domain with Lipschitz interface we show the following compactness theorem: Any -bounded sequence of vector fields with -bounded rotations and $L^2…