Nonhomogeneous variational problems and quasi-minimizers on metric spaces

Jasun Gong; Juan J. Manfredi; Mikko Parviainen

doi:10.1007/s00229-011-0489-y

Nonhomogeneous variational problems and quasi-minimizers on metric spaces

Jasun Gong^*, Juan J. Manfredi, Mikko Parviainen

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

4 Citations (Scopus)

Abstract

We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.

Original language	English
Pages (from-to)	247-271
Number of pages	25
Journal	Manuscripta Mathematica
Volume	137
Issue number	1-2
DOIs	https://doi.org/10.1007/s00229-011-0489-y
Publication status	Published - Jan 2012
MoE publication type	A1 Journal article-refereed

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@article{9e63c67d31dc41b8a3f29b7816a46f22,

title = "Nonhomogeneous variational problems and quasi-minimizers on metric spaces",

abstract = "We show that quasi-minimizers of non-homogeneous energy functionals are locally H{\"o}lder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincar{\'e} inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.",

author = "Jasun Gong and Manfredi, \{Juan J.\} and Mikko Parviainen",

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TY - JOUR

T1 - Nonhomogeneous variational problems and quasi-minimizers on metric spaces

AU - Gong, Jasun

AU - Manfredi, Juan J.

AU - Parviainen, Mikko

PY - 2012/1

Y1 - 2012/1

N2 - We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.

AB - We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.

UR - https://www.scopus.com/pages/publications/82255179276

U2 - 10.1007/s00229-011-0489-y

DO - 10.1007/s00229-011-0489-y

M3 - Article

AN - SCOPUS:82255179276

SN - 0025-2611

VL - 137

SP - 247

EP - 271

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 1-2

ER -

Nonhomogeneous variational problems and quasi-minimizers on metric spaces

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