Interpolating between torsional rigidity and principal frequency

Tom Carroll; Jesse Ratzkin

doi:10.1016/j.jmaa.2011.02.004

Interpolating between torsional rigidity and principal frequency

Tom Carroll
, Jesse Ratzkin

School of Mathematical Sciences

University of Cape Town

Research output: Contribution to journal › Article › peer-review

Abstract

A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.

Original language	English
Pages (from-to)	818-826
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	379
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.02.004
Publication status	Published - 15 Jul 2011

Keywords

Principal frequency
Semilinear partial differential equations
Sobolev embedding
Torsional rigidity

Access to Document

10.1016/j.jmaa.2011.02.004

Cite this

@article{7c532a85d0964817afabca8fe4d550c9,

title = "Interpolating between torsional rigidity and principal frequency",

abstract = "A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.",

keywords = "Principal frequency, Semilinear partial differential equations, Sobolev embedding, Torsional rigidity",

author = "Tom Carroll and Jesse Ratzkin",

year = "2011",

month = jul,

day = "15",

doi = "10.1016/j.jmaa.2011.02.004",

language = "English",

volume = "379",

pages = "818--826",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Interpolating between torsional rigidity and principal frequency

AU - Carroll, Tom

AU - Ratzkin, Jesse

PY - 2011/7/15

Y1 - 2011/7/15

N2 - A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.

AB - A one-parameter family of variational problems is examined that interpolates between torsional rigidity and the first Dirichlet eigenvalue of the Laplacian. The associated partial differential equation is derived, which is shown to have positive solutions in many cases. Results are obtained regarding extremal domains and regarding variations of the domain or the parameter.

KW - Principal frequency

KW - Semilinear partial differential equations

KW - Sobolev embedding

KW - Torsional rigidity

UR - https://www.scopus.com/pages/publications/79952818421

U2 - 10.1016/j.jmaa.2011.02.004

DO - 10.1016/j.jmaa.2011.02.004

M3 - Article

AN - SCOPUS:79952818421

SN - 0022-247X

VL - 379

SP - 818

EP - 826

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Interpolating between torsional rigidity and principal frequency

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this