Abstract
We study, in dimension n ≥ 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.
Funder
GNAMPA of INDAM
Progetto di eccellenza “Sistemi distribuiti intelligenti”of Dipartimento di Ingegneria Elettrica e dell’Informazione “M. Scarano”.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Reference37 articles.
1. On reverse Faber-Krahn inequalities
2. Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
3. Ashbaugh M.S. and
Benguria R.D., Isoperimetric inequalities for eigenvalues of the Laplacian. Spectral theory and mathematical physics: a Festschrift in honor of Barry Simon’s 60th birthday, Vol. 76.1 of
Proceedings of the Symposium on Pure Mathematics.
American Mathematical Society,
Providence, RI
(2007) 105–139.
4. A direct uniqueness proof for equations involving the p -Laplace operator
5. Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献