Existence and upper bound results for a class of nonlinear nonhomogeneous obstacle problems

Vo Minh Tam () and Shanli Liao ()
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Vo Minh Tam: Dong Thap University
Shanli Liao: Yulin Normal University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 1, 274-297

Abstract: Abstract This paper is devoted to the study of a new class of nonlinear obstacle problems involving nonhomogeneous partial differential operators and mixed boundary conditions. We provide the existence and uniqueness of the solution for the obstacle problem via applying a surjectivity theorem for set-valued mappings formulated by the sum of a set-valued pseudomonotone operator and a maximal monotone set-valued operator. Moreover, some upper bounds to the obstacle problem are established by using a regularized gap function through different norms.

Keywords: Nonhomogeneous partial differential operator; Obstacle problem; Existence; Upper bound; Clarke’s generalized gradient; 35J20; 35J25; 35J60 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-022-00362-2

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