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First we recall a Faber-Krahn type inequality and an estimate for $λ_{p} (Ω)$ in terms of the so-called Cheeger constant. Then we prove that the eigenvalue $λ_{p} (Ω)$ converges to the Cheeger constant $h (Ω)$ as $p \to 1$ . The associated eigenfunction $u_{p}$ converges to the characteristic function of the Cheeger set, i.e. a subset of $Ω$ which minimizes the ratio $| \partial D | / | D |$ among all simply connected $D \subset \subset Ω$ . As a byproduct we prove that for convex $Ω$ the Cheeger set $ω$ is also convex.

Isoperimetric inequality for an interior free boundary problem with $p$ -Laplacian operator.

Ly, Idrissa, Seck, Diaraf (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Itérés d'opérateurs elliptiques dégénérés et applications

Mohamed Salah Baouendi (1972)

Mémoires de la Société Mathématique de France

Displaying 1 – 7 of 7

Inﬁnitely many solitary waves in three space dimensions

Infinitely many solutions for the p -Laplace equations with nonsymmetric perturbations.

Infinity Laplace equation with non-trivial right-hand side.

Ipoellitticità e buona posizione del problema di Cauchy per una classe di operatori ellittici degeneri

Isoperimetric estimates for the first eigenvalue of the p -Laplace operator and the Cheeger constant

Isoperimetric inequality for an interior free boundary problem with p -Laplacian operator.

Itérés d'opérateurs elliptiques dégénérés et applications

Currently displaying 1 – 7 of 7

Infinitely many solutions for the $p$ -Laplace equations with nonsymmetric perturbations.

Isoperimetric estimates for the first eigenvalue of the $p$ -Laplace operator and the Cheeger constant

Isoperimetric inequality for an interior free boundary problem with $p$ -Laplacian operator.