On some variational problems involving capacity, torsional rigidity, perimeter and measure

Michiel van den Berg; Andrea Malchiodi

doi:10.1515/acv-2021-0076

On some variational problems involving capacity, torsional rigidity, perimeter and measure

Michiel van den Berg, Andrea Malchiodi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

We investigate the existence of a maximiser among open, bounded, convex sets in R^d , d ≥ 3 , for the product of torsional rigidity and Newtonian capacity (or logarithmic capacity if d = 2 ), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.

Original language	English
Pages (from-to)	961-974
Number of pages	14
Journal	Advances in Calculus of Variations
Volume	16
Issue number	4
DOIs	https://doi.org/10.1515/acv-2021-0076
Publication status	Published - 1 Oct 2023

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© 2022 Walter de Gruyter GmbH, Berlin/Boston 2023.

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title = "On some variational problems involving capacity, torsional rigidity, perimeter and measure",

abstract = "We investigate the existence of a maximiser among open, bounded, convex sets in Rd , d ≥ 3 , for the product of torsional rigidity and Newtonian capacity (or logarithmic capacity if d = 2 ), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.",

author = "\{van den Berg\}, Michiel and Andrea Malchiodi",

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T1 - On some variational problems involving capacity, torsional rigidity, perimeter and measure

AU - van den Berg, Michiel

AU - Malchiodi, Andrea

PY - 2023/10/1

Y1 - 2023/10/1

N2 - We investigate the existence of a maximiser among open, bounded, convex sets in Rd , d ≥ 3 , for the product of torsional rigidity and Newtonian capacity (or logarithmic capacity if d = 2 ), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.

AB - We investigate the existence of a maximiser among open, bounded, convex sets in Rd , d ≥ 3 , for the product of torsional rigidity and Newtonian capacity (or logarithmic capacity if d = 2 ), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.

U2 - 10.1515/acv-2021-0076

DO - 10.1515/acv-2021-0076

M3 - Article (Academic Journal)

SN - 1864-8266

VL - 16

SP - 961

EP - 974

JO - Advances in Calculus of Variations

JF - Advances in Calculus of Variations

IS - 4

ER -

On some variational problems involving capacity, torsional rigidity, perimeter and measure

Abstract

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