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arXiv · 2106.04702

Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities

Claudia M. Gariboldi·Stanisław Migórski·Anna Ochal·Domingo A. Tarzia
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Abstract

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.

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Claudia M. Gariboldi, Stanisław Migórski, Anna Ochal, Domingo A. Tarzia. 2021-06-08. Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities. https://arxiv.org/abs/2106.04702

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