“…Finally, this kind of estimates has been obtained also for a more general class of equations, involving the so called Finsler operator. We refer the reader, for example, to [DG,DGP1,DGP2,GT,PT,Pi].…”
In this paper we study the first Steklov-Laplacian eigenvalue with an internal fixed spherichal obstacle. We prove that the spherical shell locally maximizes the first eigenvalue among nearly spherical sets when both the internal ball and the volume are fixed.
“…Finally, this kind of estimates has been obtained also for a more general class of equations, involving the so called Finsler operator. We refer the reader, for example, to [DG,DGP1,DGP2,GT,PT,Pi].…”
In this paper we study the first Steklov-Laplacian eigenvalue with an internal fixed spherichal obstacle. We prove that the spherical shell locally maximizes the first eigenvalue among nearly spherical sets when both the internal ball and the volume are fixed.
“…Finally, we recall that in this context, estimates have been obtained also for a more general class of problems, involving the so called Finsler operator. We refer the reader, for example, to [10,12,21].…”
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional rigidity problem.
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