Regularity of optimal shapes for the Dirichlet's 
energy with volume constraint

Tanguy Briancon

Displaying similar documents to “Regularity of optimal shapes for the Dirichlet's energy with volume constraint”

On ergodic problem for Hamilton-Jacobi-Isaacs equations

Piernicola Bettiol (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the asymptotic behavior of $λ v_{λ}$ as $λ \to 0^{+}$ , where $v_{λ}$ is the viscosity solution of the following Hamilton-Jacobi-Isaacs equation (infinite horizon case) $λ v_{λ} + H (x, D v_{λ}) = 0,$ with $H (x, p) : = min_{b \in B} max_{a \in A} {- f (x, a, b) \cdot p - l (x, a, b)} .$ We discuss the cases in which the state of the system is required to stay in an -dimensional torus, called periodic boundary conditions, or in the closure of a bounded connected domain $Ω \subset^{n}$ with sufficiently smooth boundary. As far as the latter is concerned, we treat both the case of the Neumann boundary conditions (reflection...

Oscillations and concentrations in sequences of gradients

Agnieszka Kałamajska, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We use DiPerna's and Majda's generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ω; ℝ^{m \times n})$ if and $Ω \subset ℝ^{n}$ is a bounded domain with the extension property in $W^{1, p}$ . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of are required and links with lower semicontinuity...

Unique continuation property near a corner and its fluid-structure controllability consequences

Axel Osses, Jean-Pierre Puel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study a non standard unique continuation property for the biharmonic spectral problem $Δ^{2} w = - λ Δ w$ in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle $0 < θ_{0} < 2 π$ , $θ_{0} \neq π$ and $θ_{0} \neq 3 π / 2$ , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain...