21 citations · 28 across the 7 of their papers we have counts for
10 papers
On the variety of solutions of 1-dimensional nonlinear eigenvalue problems
Catherine Bandle, Simon Stingelin, Alfred Wagner
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number o…
Numerics and analysis of Cahn--Hilliard critical points
Tobias Grafke, Sebastian Scholtes, Alfred Wagner +1
We explore recent progress and open questions concerning local minima and saddle points of the Cahn--Hilliard energy in and the critical parameter regime of large system…
Symmetry of constrained minimizers of the Cahn-Hilliard energy on the torus
Michael Gelantalis, Alfred Wagner, Maria G. Westdickenberg
We establish sufficient conditions for a function on the torus to be equal to its Steiner symmetrization and apply the result to volume-constrained minimizers of the Cahn-Hilliard…
Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues
Catherine Bandle, Alfred Wagner
The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalue…
Existence and properties of certain critical points of the Cahn-Hilliard energy
Michael Gelantalis, Alfred Wagner, Maria G. Westdickenberg
The Cahn-Hilliard energy landscape on the torus is explored in the critical regime of large system size and mean value close to . Existence and properties of a "droplet-shaped"…
Optimality conditions for the buckling of a clamped plate
Kathrin Knappmann, Alfred Wagner
We prove the following uniqueness result for the buckling plate. Assume there exists a smooth domain which minimizes the first buckling eigenvalue for a plate among all smooth doma…
Domain perturbations for elliptic problems with Robin boundary conditions of opposite sign
Catherine Bandle, Alfred Wagner
We consider the energy of the torsion problem with Robin boundary conditions in the case where the solution is not a minimizer. Its dependence on the volume of the domain and the s…
Isoperimetric inequalities for the principal eigenvalue of a membrane and the energy of problems with Robin boundary conditions
Catherine Bandle, Alfred Wagner
An inequality for the reverse Bossel-Daners inequality is derived by means of the harmonic transplantation and the first shape derivative. This method is then applied to elliptic b…
Second variation of domain functionals and applications to problems with Robin boundary conditions
Catherine Bandle, Alfred Wagner
In this paper the first and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions is computed. Minimality and…
On some rescaled shape optimization problems
Giuseppe Buttazzo, Alfred Wagner
We consider Cheeger-like shape optimization problems of the form where is a given bounded domain and is above the natural scaling…