Journal für die reine und angewandte Mathematik (Crelles Journal) · 2019 · 20 citations · 25 references
Natural SciencesGeophysicsGlaciologyBoundary ConditionsEigenvalue ProblemsOperator TheorySpectral AnalysisSpectral MethodsSpectral TheoryDirichlet Boundary ConditionsDirichlet ProblemsDirichlet ProcessesEigenfunction ExpansionsEigenvalues Of The LaplacianLipschitz ConditionsSpectral ApproximationSpectral Asymptotics
Abstract We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.
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COVARIANT AND CONTRAVARIANT SYMBOLS OF OPERATORS
F. A. Berezin · Mathematics of the USSR-Izvestiya · 1972 · 493 citations