Singular double-phase systems with variable growth for the Baouendi-Grushin operator
type: Item
instance of: scholarly article
title: Singular double-phase systems with variable growth for the Baouendi-Grushin operator
zbMATH Open document ID: 1467.35163
author: Anouar Bahrouni
author: Vicenţiu D. Rădulescu
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-06-08T00:00:00Z
review text: The authors study a double-phase system of equations involving a singular term in the reaction, in the whole space \(\mathbb{R}^N\). The principal operator is the Baouendi-Grushin operator with variable coefficient, which is defined by \[\Delta_{G(x,y)}u= \sum_{i=1}^{n}\left(|\nabla_x|^{G(x,y)-2}u_{x_i} \right)_{x_i}+|x|^\gamma \sum_{i=1}^{n}\left(|\nabla_y|^{G(x,y)-2}u_{y_i} \right)_{y_i},\] where \(G:\mathbb{R}^N \to (1,\infty)\) is a continuous function. After discussing some properties concerning this operator, the authors prove the existence of a weak solution to the double-phase system. The result is established by monotonicity arguments. The similar operator in the context of a class of double-phase energy functionals arising in the theory of transonic flows, was previously studied in a bounded domain \(\Omega \subset \mathbb{R}^N\) (\(N\geq 2\)) with smooth boundary \(\partial \Omega\), by the authors et al. [Nonlinearity 32, No. 7, 2481--2495 (2019; Zbl 1419.35056)].
reviewed by: Calogero Vetro
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35P30
Mathematics Subject Classification ID: 76H05
zbMATH DE Number: 7356648
zbMATH Keywords: Baouendi-Grushin operator
zbMATH Keywords: double-phase problem
zbMATH Keywords: singular term
zbMATH Keywords: degenerate differential operator
zbMATH Keywords: existence of solutions
MaRDI profile type: Publication
full work available at URL: dcds.2021036
OpenAlex ID: W3128175575
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DOI: 10.3934/DCDS.2021036
description: scientific article; zbMATH DE number 7356648