Partial regularity results for non-autonomous functionals with Φ-growth conditions

被引：0

作者：

Giannetti, Flavia ^{[1
]}

di Napoli, Antonia Passarelli ^{[1
]}

Tachikawa, Atsushi ^{[2
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Appl R Caccioppoli, Via Cintia, I-80126 Naples, Italy

[2] Tokyo Univ Sci, Fac Sci & Technol, Dept Math, Noda, Chiba 2788510, Japan

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2017年 / 196卷 / 06期

关键词：

Partial regularity; Nonstandard growth; Non-autonomous functionals; HOLDER CONTINUITY; ELLIPTIC-SYSTEMS; MINIMIZERS; INTEGRALS; EXISTENCE; EQUATIONS; GRADIENT;

D O I：

10.1007/s10231-017-0658-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the partial Holder continuity of the local minimizers of non-autonomous integral functionals of the type integral(Omega) Phi((A(ij)(alpha beta)(x, u)D(i)u(alpha)D(j)u(beta))(1/2))dx, where is an Orlicz function satisfying both the Delta(2) and del(2) conditions and the function is uniformly elliptic, bounded and continuous. Assuming in addition that the function is Holder continuous, we prove the partial Holder continuity also of the gradient of the local minimizers.

引用

页码：2147 / 2165

页数：19

共 38 条

[31]

Giova R, 2016, NODEA-NONLINEAR DIFF, V23, DOI 10.1007/s00030-016-0419-5

[32] Everywhere regularity for a class of vectorial functionals under subquadratic general growth conditions [J].

Leonetti, F ;

Mascolo, E ;

Siepe, F .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 287 (02) :593-608

[33] Nonlinear elliptic systems with general growth [J].

Marcellini, P ;

Papi, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 221 (02) :412-443

[34] REGULARITY AND EXISTENCE OF SOLUTIONS OF ELLIPTIC-EQUATIONS WITH P,Q-GROWTH CONDITIONS [J].

MARCELLINI, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 90 (01) :1-30

[35]

Marcellini P., 1996, Annali Della Scuola Normale di Pisa, V23, P1

[36]

Ragusa MA, 2013, NONLINEAR ANAL-THEOR, V93, P162, DOI 10.1016/j.na.2013.07.023

[37]

Ragusa MA, 2013, T AM MATH SOC, V365, P3329

[38]

SHIKOV VV, 1995, RUSS J MATH PHYS, V3, P249

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