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Some further results on the nonlocal p-Laplacian type problems

Part of: Representations of solutions Elliptic equations and systems Parabolic equations and systems

Published online by Cambridge University Press:  07 August 2020

Chao Zhang  and
Xia Zhang
Chao Zhang
Affiliation:
School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin150001, PR China (czhangmath@hit.edu.cn)
Xia Zhang
Affiliation:
School of Mathematics, Harbin Institute of Technology, Harbin150001, PR China (zhangxia@hit.edu.cn)
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Abstract

We study the existence of entropy solutions by assuming the right-hand side function f to be an integrable function for some elliptic nonlocal p-Laplacian type problems. Moreover, the existence of weak solutions for the corresponding parabolic cases is also established. The main aim of this paper is to provide some positive answers for the two questions proposed by Chipot and de Oliveira (Math. Ann., 2019, 375, 283-306).

Keywords

Nonlocal p-Laplacian type problemsentropy solutionsweak solutionsexistence

MSC classification

Primary: 35J60: Nonlinear elliptic equations 35K61: Nonlinear initial-boundary value problems for nonlinear parabolic equations
Secondary: 35D30: Weak solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 3 , June 2021 , pp. 953 - 970
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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