Rayleigh Principle for Stratified Laplacian

Authors

DOI:

https://doi.org/10.52575/2687-0959-2024-56-3-175-180

Keywords:

Stratified Set, Laplacian, Dirichlet Problem, Rayleigh Principle

Abstract

In this paper we give an exact analog of Rayleigh principle for laplacians on stratified sets. Our main result may be applied for an estimation of the first eigenvalue of stratified laplacian equipped with Dirichlet conditon. Previous results on this subject were known for one dimensional stratified sets and for a specific laplacian, called 'soft laplacian', defined on multidimensional stratified sets. Meanwhile there is a variety of laplacians on stratified sets. Our results are valid for all stratified laplacians without any restrictions on the dimension.

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Author Biographies

Sofia N. Oshchepkova, Voronezh State University of Engineering Technologies

Candidate of Physical and Mathematical Sciences, Assosiate Professor of the Chair of Higher
Mathematics, Voronezh State University of Engineering Technologies,
Voronezh, Russia

E-mail: osonia@mail.ru
ORCID: 0000-0001-9555-541X

Oleg M. Penkin, Voronezh State University

Doctor of Physical and Mathematical Sciences, Professor, Professor, Professor of the Chair of Mathematical Modelling, Voronezh State University,
Voronezh, Russia

E-mail: o.m.penkin@gmail.com
ORCID: 0000-0001-9547-7597

Sergey L. Tsarev, Voronezh State University

Candidate of Physical and Mathematical Sciences, Assosiate Professor of the Chair of Mathematical Modelling, Voronezh State University,
Voronezh, Russia

E-mail: s@tzareff.ru
ORCID: 0009-0001-2957-9269

References

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Published

2024-09-30

How to Cite

Oshchepkova, S. N., Penkin, O. M., & Tsarev, S. L. (2024). Rayleigh Principle for Stratified Laplacian. Applied Mathematics & Physics, 56(3), 175-180. https://doi.org/10.52575/2687-0959-2024-56-3-175-180

Issue

Vol. 56 No. 3 (2024)

Section

Mathematics

Copyright (c) 2024 Applied Mathematics & Physics

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