Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces

PRASHANTA GARAIN; JUHA KINNUNEN

doi:10.1090/proc/15417

Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces

PRASHANTA GARAIN^*, JUHA KINNUNEN

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

Original language	English
Pages (from-to)	3407-3416
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	8
DOIs	https://doi.org/10.1090/proc/15417
Publication status	Published - Aug 2021
MoE publication type	A1 Journal article-refereed

Keywords

Analysis on metric measure spaces
Energy estimate
Minimizer
Newtonian space
Nonexistence
Variational integral

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10.1090/proc/15417

https://arxiv.org/abs/2009.03773

Cite this

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title = "Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces",

abstract = "In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincar{\'e} inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.",

keywords = "Analysis on metric measure spaces, Energy estimate, Minimizer, Newtonian space, Nonexistence, Variational integral",

author = "PRASHANTA GARAIN and JUHA KINNUNEN",

year = "2021",

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AU - GARAIN, PRASHANTA

AU - KINNUNEN, JUHA

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N2 - In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

AB - In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

KW - Analysis on metric measure spaces

KW - Energy estimate

KW - Minimizer

KW - Newtonian space

KW - Nonexistence

KW - Variational integral

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M3 - Article

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EP - 3416

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces

Abstract

Keywords

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