Eigenvalues for double phase variational integrals

被引：193
作者：
Colasuonno, Francesca [2 ]
Squassina, Marco [1 ]
机构：
[1] Univ Verona, Dipartimento Informat, Ca Vignal 2,Str Le Grazie 15, I-37134 Verona, Italy
[2] CNR, Ist Applicaz Calcolo M Picone, Via Taurini 19, I-00185 Rome, Italy
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 06期
关键词：
Quasilinear problems; Double phase problems; Nonstandard growth conditions; Musielak-Orlicz spaces; Gamma-convergence; Stability of eigenvalues; Weyl-type laws; ASYMPTOTIC-BEHAVIOR; P-LAPLACIAN; ELLIPTIC-EQUATIONS; REGULARITY; FUNCTIONALS; CONTINUITY; STABILITY; MINIMIZERS; EXISTENCE; CALCULUS;
D O I：
10.1007/s10231-015-0542-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study an eigenvalue problem in the framework of double phase variational integrals, and we introduce a sequence of nonlinear eigenvalues by a minimax procedure. We establish a continuity result for the nonlinear eigenvalues with respect to the variations of the phases. Furthermore, we investigate the growth rate of this sequence and get a Weyl-type law consistent with the classical law for the p-Laplacian operator when the two phases agree.
引用
收藏
页码：1917 / 1959
页数：43
相关论文
共 63 条
  • [1] Regularity results for a class of functionals with non-standard growth
    Acerbi, E
    Mingione, G
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) : 121 - 140
  • [2] Acerbi E., 2001, Ann. Sc. Norm. Super. Pisa, Cl. Sci., V30, P311
  • [3] [Anonymous], 2010, Morse Theoretic Aspects of p-Laplacian Type Operators. Mathematical surveys and monographs
  • [4] [Anonymous], PREPRINT
  • [5] [Anonymous], 2012, Homogenization of differential operators and integral functionals
  • [6] [Anonymous], ERGEBNISSE MATH
  • [7] [Anonymous], 1945, THEORY SOUND
  • [8] [Anonymous], 1953, Methods of mathematical physics
  • [9] [Anonymous], 2010, FUNCTIONAL ANAL
  • [10] [Anonymous], 2006, Report
1234567