Harnack inequality and continuity of solutions to elliptic equations with nonstandard growth conditions and lower order terms

被引：0
作者：
Vitali Liskevich
Igor I. Skrypnik
机构：
[1] Swansea University,Department of Mathematics
[2] Institute of Applied Mathematics and Mechanics,undefined
来源：
Annali di Matematica Pura ed Applicata | 2010年 / 189卷
关键词：
Equations with nonstandard growth conditions; Harnack inequality; Continuity; Nonlinear Kato-class; 35J60 (35B05, 35B65);
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove the Harnack inequality and continuity of solutions for a general class of divergence-type elliptic equations with nonstandard growth measurable coefficients in the main part and lower order terms from nonlinear Kato-type classes.
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页码：335 / 356
页数：21
相关论文
共 27 条
[1]  
Acerbi E.(2001)Regularity results for a class of functionals with non-standard growth Arch. Ration. Mech. Anal. 156 121-140
[2]  
Mingione G.(1982)Brownian motion and Harnack inequality for Schrödinger operators Commun. Pure Appl. Math. 35 209-273
[3]  
Aizenman M.(1997)The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition (Russian) Differ. Uravn. 33 1651-1660
[4]  
Simon B.(2004)Continuity at boundary points of solutions of quasilinear elliptic equations with a nonstandard growth condition (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 68 3-60
[5]  
Alkhutov Y.A.(1997)Nonlinear Kato measures and nonlinear subelliptic Schrödinger problems Rend. Acad. Naz. Sci. XL Mem. Math. Appl. 21 235-252
[6]  
Alkhutov Y.A.(2001)Schrödinger type and relaxed Dirichlet problems for the subelliptic Potential Anal. 15 1-16
[7]  
Krasheninnikova O.V.(1997)-Laplacian Manuscr. Math. 93 283-299
[8]  
Biroli M.(1986)Hölder continuity of minimizers of functionals with variable growth exponent Proc. Am. Math. Soc. 98 415-425
[9]  
Biroli M.(1999)Harnack’s inequality for Schrödinger operators and the continuity of solutions Nonlinear Anal. TMA 36 295-318
[10]  
Chiadò Piat V.(2001)A class of De Giorgi type and Hölder continuity J. Math. Anal. Appl. 263 424-446
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