Minimization of the zeroth Neumann eigenvalues with integrable potentials
نویسندگان
چکیده
منابع مشابه
Minimization of the zeroth Neumann eigenvalues with integrable potentials
For an integrable potential q on the unit interval, let λ0(q) be the zeroth Neumann eigenvalue of the Sturm–Liouville operator with the potential q. In this paper we will solve the minimization problem L̃1(r) = infq λ0(q), where potentials q have mean value zero and L1 norm r . The final result is L̃1(r)=−r/4. The approach is a combination of variational method and limiting process, with the help...
متن کاملMinimization of Eigenvalues of One-Dimensional p-Laplacian with Integrable Potentials
In this paper, we will use the variational method and limiting approach to solve the minimization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian when the L1 norm of integrable potentials is given. Combining with the results for the corresponding maximization problems, we have obtained the explicit results for these eigenvalues.
متن کاملNeumann-like integrable models
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (Hn, In) are exhibited. For n = 1 we recover Neumann sytem on T ∗ S2. All these systems are also integrable at the quantum level.
متن کاملMAXIMIZATION OF EIGENVALUES OF ONE-DIMENSIONAL p-LAPLACIAN WITH INTEGRABLE POTENTIALS
In this paper we will use variational methods and limiting approaches to give a complete solution to the maximization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian with integrable potentials of fixed L 1-norm.
متن کاملMaximising Neumann eigenvalues on rectangles
We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in R with a measure or perimeter constraint. We show that the rectangle with measure 1 which maximises the k’th Neumann eigenvalue converges to the unit square in the Hausdorff metric as k → ∞. Furthermore, we determine the unique maximiser of the k’th Neumann eigenvalue on a rectangle with given perimeter. AMS...
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: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2012
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2012.01.007