Remarks on the Harnak Inequality for Local-Minima of Scalar Integral Functionals with General Growth Conditions

Granucci, Tiziano

doi:10.4236/jamp.2014.25024

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Cited by 2 publications

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“…with 0 < c 7 < c 8 . In [9] and [10] T. Granucci has extended, partially, the precedents results. Moreover in [12] V. S. Klimov studies this problem when Φ satisfies ∇ 2 but not a 2 condition.…”

Section: Introductionmentioning

confidence: 76%

Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions

Granucci¹

2015

nade

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In this paper we show a regularity theorem for quasi-minima of scalar integral functionals of the Calculus of Variations with nonstandard growth conditions. Let us consider functionals as the following form F [u, Ω] = Ω f (x, u (x) , ∇u (x)) dx where f : Ω × R × R N → R is a Carathéodory function satisfying the inequalities |z| p − c 1 ≤ f (x, s, z) ≤ c 2 |z| βp * + |s| βp * + 1 for each z ∈ R N , s ∈ R and for L N-a. e. x ∈ Ω, where c 1 and c 2 are two positive real constants, with c 1 < c 2 , Ω is an open subset of R N , N ≥ 2, 1 < p < N and p p * < β <β p,N ≤ 1 where p * = N p N −p is the Sobolev conjugate of p andβ p,N is a positive real number.

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Section: Introductionmentioning

confidence: 76%

Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions

Granucci¹

2015

nade

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A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions

Granucci

2016

manuscripta math.

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Remarks on the Harnak Inequality for Local-Minima of Scalar Integral Functionals with General Growth Conditions

Abstract: In this paper we proof a Harnack inequality and a regularity theorem for local-minima of scalar intagral functionals with general growth conditions.

Cited by 2 publications

References 21 publications

Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions

Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions

A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions

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