On the error in the two-term Weyl formula for the Dirichlet Laplacian

Frank, Rupert L. und Larson, Simon (2020): On the error in the two-term Weyl formula for the Dirichlet Laplacian. In: Journal of Mathematical Physics, Bd. 61, Nr. 4

Abstract

We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of Rd. In particular, for the short-time asymptotics of the trace of the heat kernel, we prove that the error term cannot be made quantitatively better than little-o of the second term.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Analysis, Mathematische Physik und Numerik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0022-2488
• Sprache: Englisch