Nonlinear nonhomogeneous obstacle problems with multivalued convection term
type: Item
instance of: scholarly article
title: Nonlinear nonhomogeneous obstacle problems with multivalued convection term
zbMATH Open document ID: 1485.35160
author: Yunru Bai
author: Leszek Gasiński
author: Sheng-Da Zeng
published in: The Journal of Geometric Analysis
publication date: 2022-02-10T00:00:00Z
review text: The authors consider an obstacle problem of the form \begin{align*} \begin{cases} -\text{div}\ a(x,\nabla u)\in f(x,u,\nabla u)& \text{in }\Omega,\\ u\leq \Phi &\text{in }\Omega,\\ u=0&\text{on }\partial\Omega, \end{cases} \end{align*} where \(a\colon\overline{\Omega}\times\mathbb{R}^N\to\mathbb{R}^N\) is continuous and satisfies suitable structure conditions, \(\Phi\colon \Omega\to [0,+\infty]\) is a given obstacle and \(f\colon\Omega\times\mathbb{R}\times\mathbb{R}^N\to2^{\mathbb{R}}\) is a multivalued function depending on the gradient of the solution satisfying appropriate growth and coercivity properties. The main result in this paper shows that the solution set of the problem above is nonempty, bounded and closed. Its proof is based on the surjectivity theorem for multivalued functions given by the sum of a maximal monotone multivalued operator and a bounded multivalued pseudomonotone one.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 7472159
zbMATH Keywords: nonhomogeneous partial differential operator
zbMATH Keywords: multivalued convection term
zbMATH Keywords: generalized pseudomonotone operators
zbMATH Keywords: existence
MaRDI profile type: Publication
full work available at URL: s12220-021-00821-y
OpenAlex ID: W4205193872
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DOI: 10.1007/S12220-021-00821-Y
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description: scientific article; zbMATH DE number 7472159