A Weyl law for the p-Laplacian

We show that a Weyl law holds for the variational spectrum of the p-Laplacian. More precisely, let (lambda(i))(i=1)(infinity) be the variational spectrum of Delta(p) on a closed Riemannian manifold (X, g) and let N(lambda) = #{i: lambda(i )< lambda} be the associated counting function. Then we have a Weyl law N(lambda)similar to c vol(X)lambda(n/p). This confirms a conjecture of Friedlander. The proof is based on ideas of Gromov [5] and Liokumovich, Marques, Neves [7]. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.