Convex shape optimization for the least biharmonic Steklov eigenvalue
نویسندگان
چکیده
منابع مشابه
The first biharmonic Steklov eigenvalue: positivity preserving and shape optimization
We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure. Mathematics Subject Classification (2000)....
متن کاملOptimization of the First Steklov Eigenvalue in Domains with Holes: a Shape Derivative Approach
The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. We deal with minimizers of the Rayleigh quotient ‖u‖2 H1(Ω) /‖u‖2 L2(∂Ω) for functions that vanish in a subset A ⊂ Ω, which we call the hole. We look for holes that minimize the best Sobolev trace constant among subsets of Ω with prescribed volume. First, we find a formula for the first variation of the ...
متن کاملOn Positivity for the Biharmonic Operator under Steklov Boundary Conditions
The positivity-preserving property for the inverse of the biharmonic operator under Steklov boundary conditions is studied. It is shown that this property is quite sensitive to the parameter involved in the boundary condition. Moreover, positivity of the Steklov boundary value problem is linked with positivity under boundary conditions of Navier and Dirichlet type.
متن کاملA two-grid discretization scheme for the Steklov eigenvalue problem
In the paper, a two-grid discretization scheme is discussed for the Steklov eigenvalue problem. With the scheme, the solution of the Steklov eigenvalue problem on a fine grid is reduced to the solution of the Steklov eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. Using spectral approximation theory, it is shown theoretically that the tw...
متن کاملA Posteriori Error Estimates for the Steklov Eigenvalue Problem
In this paper we introduce and analyze an a posteriori error estimator for the linear finite element approximations of the Steklov eigenvalue problem. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, up to higher order terms, the estimator is equivalent to the energy norm of the error. Finally, we prove that the vo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2013
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv/2012014