A general regularity theorem for functionals with phi-growth

Dominic Breit; Bianca Stroffolini; Anna Verde

doi:10.1016/j.jmaa.2011.05.012

A general regularity theorem for functionals with phi-growth

Dominic Breit, Bianca Stroffolini^*, Anna Verde

^*Corresponding author for this work

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

25 Citations (Scopus)

Abstract

We prove C(1,alpha)-regularity for local minimizers of functionals

integral(Omega)phi vertical bar del u vertical bar)dx,

where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	226-233
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	383
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2011.05.012
Publication status	Published - Nov 2011

Keywords

Vector-valued problems
Local minimizers
Nonstandard growth
Regularity
NONLINEAR ELLIPTIC-SYSTEMS
VARIATIONAL INTEGRALS
MINIMIZERS

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title = "A general regularity theorem for functionals with phi-growth",

abstract = "We prove C(1,alpha)-regularity for local minimizers of functionalsintegral(Omega)phi vertical bar del u vertical bar)dx,where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.",

keywords = "Vector-valued problems, Local minimizers, Nonstandard growth, Regularity, NONLINEAR ELLIPTIC-SYSTEMS, VARIATIONAL INTEGRALS, MINIMIZERS",

author = "Dominic Breit and Bianca Stroffolini and Anna Verde",

year = "2011",

month = nov,

doi = "10.1016/j.jmaa.2011.05.012",

language = "English",

volume = "383",

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T1 - A general regularity theorem for functionals with phi-growth

AU - Breit, Dominic

AU - Stroffolini, Bianca

AU - Verde, Anna

PY - 2011/11

Y1 - 2011/11

N2 - We prove C(1,alpha)-regularity for local minimizers of functionalsintegral(Omega)phi vertical bar del u vertical bar)dx,where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.

AB - We prove C(1,alpha)-regularity for local minimizers of functionalsintegral(Omega)phi vertical bar del u vertical bar)dx,where phi is a Young function. In order to generalize the results of Fuchs (2011) [9] and Diening et al. (2009) [6], we assume for the function phi only the (Delta 2)-condition and phi ''(t) >= (epsilon) over cap phi'(t)/t for a positive constant (epsilon) over cap (and derivatives). of course a Holder-condition for the second (C) 2011 Elsevier Inc. All rights reserved.

KW - Vector-valued problems

KW - Local minimizers

KW - Nonstandard growth

KW - Regularity

KW - NONLINEAR ELLIPTIC-SYSTEMS

KW - VARIATIONAL INTEGRALS

KW - MINIMIZERS

U2 - 10.1016/j.jmaa.2011.05.012

DO - 10.1016/j.jmaa.2011.05.012

M3 - Article

SN - 0022-247X

VL - 383

SP - 226

EP - 233

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A general regularity theorem for functionals with phi-growth

Abstract

Keywords

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