Regularity of minimizers under limit growth conditions

被引：45
作者：
Cupini, Giovanni [1 ]
Marcellini, Paolo [2 ]
Mascolo, Elvira [2 ]
机构：
[1] Univ Bologna, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy
[2] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 153卷
关键词：
Anisotropic growth condition; Local boundedness; Non-coercive functional; LOCAL BOUNDEDNESS; FUNCTIONALS; EXISTENCE; INTEGRALS; CALCULUS; MINIMA;
D O I：
10.1016/j.na.2016.06.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is well known that an integral of the Calculus of Variations satisfying anisotropic growth conditions may have unbounded minimizers if the growth exponents are too far apart. Under sharp assumptions on the exponents we prove the local boundedness of minimizers of functionals with anisotropic p, q-growth,via the De Giorgi method. As a by-product, regularity of minimizers of some non coercive functionals is obtained by reduction to coercive ones. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：294 / 310
页数：17
相关论文
共 31 条
[11]   HIGHER INTEGRABILITY FOR MINIMIZERS OF ANISOTROPIC FUNCTIONALS [J].
Carozza, Menita ;
Moscariello, Gioconda ;
Di Napoli, Antonia Passarelli .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2009, 11 (01) :43-55
[12]   Bounded Minimisers of Double Phase Variational Integrals [J].
Colombo, Maria ;
Mingione, Giuseppe .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 218 (01) :219-273
[13]   Regularity for Double Phase Variational Problems [J].
Colombo, Maria ;
Mingione, Giuseppe .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 215 (02) :443-496
[14]   On the continuity of solutions to degenerate elliptic equations [J].
Cruz-Uribe, D. ;
Di Gironimo, P. ;
Sbordone, C. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (06) :2671-2686
[15]   REGULARITY UNDER SHARP ANISOTROPIC GENERAL GROWTH CONDITIONS [J].
Cupini, Giovanni ;
Marcellini, Paolo ;
Mascolo, Elvira .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2009, 11 (01) :67-86
[16]   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
[17]   Local boundedness of solutions to some anisotropic elliptic systems [J].
Cupini, Giovanni ;
Marcellini, Paolo ;
Mascolo, Elvira .
RECENT TRENDS IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS II: STATIONARY PROBLEMS, 2013, 595 :169-+
[18]   Local boundedness of solutions to quasilinear elliptic systems [J].
Cupini, Giovanni ;
Marcellini, Paolo ;
Mascolo, Elvira .
MANUSCRIPTA MATHEMATICA, 2012, 137 (3-4) :287-315
[19]  
De Giorgi E., 1957, Mem. Acad. Sci. Torino. Cl. Sci. Fis. Mat. Nat., V3, P25
[20]   VARIATIONAL PRINCIPLE [J].
EKELAND, I .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) :324-353
1234