A new weighted Friedrichs--type inequality for a perforated domain with a sharp constant


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Authors

  • Gregory A. Chechkin
  • Yulia O. Koroleva
  • Lars-Erik Persson
  • Peter Wall

Keywords:

partial differential equations, functional analysis, spectral theory, homogenization theory, Hardy-type inequalities, Friedrichs-type inequalities

Abstract

We derive a new three-dimensional Hardy-type inequality for a cube for the class of functions from the Sobolev space H1 having zero trace on small holes distributed periodically along the boundary. The proof is based on a careful analysis of the asymptotic expansion of the first eigenvalue of a related spectral problem and the best constant of the corresponding Friedrichs-type inequality.

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Published

2024-05-26

How to Cite

Chechkin, G. A., Koroleva, Y. O., Persson, L.-E., & Wall, P. (2024). A new weighted Friedrichs--type inequality for a perforated domain with a sharp constant. Eurasian Mathematical Journal, 2(1). Retrieved from https://emj.enu.kz/index.php/main/article/view/70

Issue

Vol. 2 No. 1 (2011)

Section

Articles