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REILLY-TYPE UPPER BOUNDS FOR THE p-STEKLOV PROBLEM ON SUBMANIFOLDS

Part of: Calculus on manifolds; nonlinear operators Spectral theory and eigenvalue problems Global differential geometry Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  28 February 2023

JULIEN ROTH Open the ORCID record for JULIEN ROTH [Opens in a new window]  and
ABHITOSH UPADHYAY Open the ORCID record for ABHITOSH UPADHYAY [Opens in a new window]
JULIEN ROTH
Affiliation:
Université Gustave Eiffel, CNRS, LAMA UMR 8050, F-77447 Marne-la-Vallée, France e-mail: julien.roth@univ-eiffel.fr
ABHITOSH UPADHYAY*
Affiliation:
School of Mathematics and Computer Science, Indian Institute of Technology, Goa 403401, India
*
e-mail: abhitosh@iitgoa.ac.in
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Abstract

We prove Reilly-type upper bounds for the first nonzero eigenvalue of the Steklov problem associated with the p-Laplace operator on submanifolds of manifolds with sectional curvature bounded from above by a nonnegative constant.

Keywords

p-LaplacianSteklov problemeigenvalues

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 58C40: Spectral theory; eigenvalue problems 58J32: Boundary value problems on manifolds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 3 , December 2023 , pp. 492 - 503
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The second author gratefully acknowledges the financial support from the Indian Institute of Technology Goa through Start-up Grant 2021/SG/AU/043.

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