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Mathematics > Analysis of PDEs

arXiv:1810.07995 (math)
[Submitted on 18 Oct 2018]

Title:Double phase problems with variable growth

Authors:Matija Cencelj, Vicenţiu D. Rădulescu, Dušan D. Repovš
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Abstract:We consider a class of double phase variational integrals driven by nonhomogeneous potentials. We study the associated Euler equation and we highlight the existence of two different Rayleigh quotients. One of them is in relationship with the existence of an infinite interval of eigenvalues while the second one is associated with the nonexistence of eigenvalues. The notion of eigenvalue is understood in the sense of pairs of nonlinear operators, as introduced by Fučik, Nečas, Souček, and Souček. The analysis developed in this paper extends the abstract framework corresponding to some standard cases associated to the $p(x)$-Laplace operator, the generalized mean curvature operator, or the capillarity differential operator with variable exponent. The results contained in this paper complement the pioneering contributions of Marcellini, Mingione et al. in the field of variational integrals with unbalanced growth.
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35J60, 35P30, 47J10, 58C40, 58E30
Cite as: arXiv:1810.07995 [math.AP]
  (or arXiv:1810.07995v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1810.07995
Journal reference: Nonlinear Anal. 177 (2018), Part A, 270-287
Related DOI: https://doi.org/10.1016/j.na.2018.03.016

Submission history

From: Dušan Repovš [view email]
[v1] Thu, 18 Oct 2018 11:36:07 UTC (18 KB)
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