Sharp estimates for the first <i>p</i>-Laplacian eigenvalue and for the <i>p</i>-torsional rigidity on convex sets with holes
Gloria Paoli, Gianpaolo Piscitelli, Leonardo Trani
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.
Topics & Concepts
Eigenvalues and eigenvectorsRigidity (electromagnetism)MathematicsLaplace operatorRegular polygonMathematical analysisPerimeterp-LaplacianBoundary value problemBoundary (topology)CombinatoricsGeometryPhysicsQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringGeometric Analysis and Curvature Flows