How to prove existence in shape optimization
Boundary variation for a Neumann problem
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetric-like inequalities. As a byproduct...
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...
The eigenvalue problem with conductivity boundary conditions
Boundary optimization under pseudo curvature constraint
Optimal convex shapes for concave functionals
Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application...
Wall laws for viscous fluids near rough surfaces
In this paper, we review recent results on wall laws for viscous fluids near rough
surfaces, of small amplitude and wavelength
Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients.
Spectrum stability of an elliptic operator to domain perturbations.
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