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The aim of this paper is to give a complementary upper bound-type isoperimetric inequality for the fundamental Dirichlet eigenvalue of a bounded domain completely contained in a cone. This inequality… Click to show full abstract
The aim of this paper is to give a complementary upper bound-type isoperimetric inequality for the fundamental Dirichlet eigenvalue of a bounded domain completely contained in a cone. This inequality is a counterpart to the Ratzkin inequality for Euclidean wedge domains in higher dimensions. We also give a new version of the Crooke–Sperb inequality involving a new geometric quantity for the first eigenfunction of the Dirichlet Laplacian for such a class of domains.
Keywords:
inequality;
dirichlet eigenvalue;
sharp upper;
upper bound;
bound first
Journal Title: Archiv der Mathematik
Year Published: 2020
Link to full text (if available)
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Journal Title: Archiv der Mathematik
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!