4 papers
An abstract lagrangian framework for computing shape derivatives
Antoine Laurain, Pedro T. P. Lopes, Jean C. Nakasato
In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit functi…
Spectral Invariance of Pseudodifferential Boundary Value Problems on Manifolds with Conical Singularities
Pedro T. P. Lopes, Elmar Schrohe
We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the Lp-setting. As a consequence…
Dynamical boundary conditions in a non-cylindrical domain for the Laplace equation
Pedro T. P. Lopes, Marcone C. Pereira
In this paper, we study existence, uniqueness and asymptotic behavior of the Laplace equation with dynamical boundary conditions on regular non-cylindrical domains. We write the pr…
The regularity of the function for the Shubin calculus
Pedro Lopes
We prove the regularity of the function for classical pseudodifferential operators with Shubin symbols. We recall the construction of complex powers and of the Wodzicki and Kon…