A Comparison Theorem for the First Non-zero Steklov Eigenvalue

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the First Eigenvalue of a Fourth Order Steklov Problem

We prove some results about the first Steklov eigenvalue d1 of the biharmonic operator in bounded domains. Firstly, we show that Fichera’s principle of duality [9] may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d1 for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problem...

متن کامل

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 کامل

A 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 کامل

A 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 کامل

Optimization 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 کامل

ذخیره 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: Journal of Functional Analysis

سال: 2000

ISSN: 0022-1236

DOI: 10.1006/jfan.2000.3662