ON THE REGULARITY OF MINIMIZERS FOR SCALAR INTEGRAL FUNCTIONALS WITH (p, q)-GROWTH

被引：38

作者：

Bella, Peter ^{[1
]}

Schaeffner, Mathias ^{[2
]}

机构：

[1] Tech Univ Dortmund, Fak Math, Dortmund, Germany

[2] Univ Leipzig, Math Inst, Leipzig, Germany

来源：

ANALYSIS & PDE | 2020年 / 13卷 / 07期

关键词：

nonuniformly elliptic equations; local Lipschitz continuity; (p; q)-growth; nonstandard growth conditions; ELLIPTIC-EQUATIONS;

D O I：

10.2140/apde.2020.13.2241

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We revisit the question of regularity for minimizers of scalar autonomous integral functionals with so-called (p, q)-growth. In particular, we establish Lipschitz regularity under the condition q/p < 1 + 2/n-1 for n >= 3, improving a classical result due to Marcellini (J. Differential Equations 90:1 (1991), 1-30).

引用

收藏

页码：2241 / 2257

页数：17

相关论文

共 27 条

[1] Regularity for general functionals with double phase [J].

Baroni, Paolo ;

Colombo, Maria ;

Mingione, Giuseppe .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (02)

[2] Lipschitz Bounds and Nonuniform Ellipticity [J].

Beck, Lisa ;

Mingione, Giuseppe .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2020, 73 (05) :944-1034

[3]

Bella P., COMM PURE APPL MATH

[4] QUENCHED INVARIANCE PRINCIPLE FOR RANDOM WALKS AMONG RANDOM DEGENERATE CONDUCTANCES [J].

Bella, Peter ;

Schaffner, Mathias .

ANNALS OF PROBABILITY, 2020, 48 (01) :296-316

[5] Lipschitz regularity for orthotropic functionals with nonstandard growth conditions [J].

Bousquet, Pierre ;

Brasco, Lorenzo .

REVISTA MATEMATICA IBEROAMERICANA, 2020, 36 (07) :1989-2032

[6]

Carozza M, 2014, ANN SCUOLA NORM-SCI, V13, P1065

[7] Higher differentiability of minimizers of convex variational integrals [J].

Carozza, Menita ;

Kristensen, Jan ;

di Napoli, Antonia Passarelli .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2011, 28 (03) :395-411

[8] Regularity for Double Phase Variational Problems [J].

Colombo, Maria ;

Mingione, Giuseppe .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 215 (02) :443-496

[9] Local Boundedness of Minimizers with Limit Growth Conditions [J].

Cupini, Giovanni ;

Marcellini, Paolo ;

Mascolo, Elvira .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 166 (01) :1-22

[10] On the Regularity of Minima of Non-autonomous Functionals [J].

De Filippis, Cristiana ;

Mingione, Giuseppe .

JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (02) :1584-1626