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math.AP2025
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…
math.AP2024
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…