Well-posedness and convergence results for elliptic hemivariational inequalities

• Autores: Sofonea, Mircea; Tarzia, Domingo Alberto
• Año de publicación: 2025
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Well-posed problem; Convergence results; Elliptic hemivariational inequalities
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We consider an elliptic hemivariational inequality in a real reflexive Banach space X which, under appropriate assumptions on the data, has a unique solution u ∈ X. We recall the concepts of wellposedness in the sense of Tykhonov and Levitin-Polyak for this inequality, and then we extend these concepts by introducing new well-posedness concepts, constructed with a larger set of approximating sequences. We also prove that, under additional assumptions, these new well-posedness concepts are optimal in the sense that all the sequences of elements of X which converge to the solution u are approximating sequences. This result, presented in Theorem 4.1, provides necessary and sufficient conditions for any sequence {un} ⊂ X which guarantees that it converges to u and, therefore, it represents a convergence criterion to the solution of the hemivariational inequality. This criterion can be used in various applications. To provide an example, we illustrate its use in the study of a penalty method associated to an elliptic hemivariational inequality which describes the equilibrium of an elastic membrane in contact with a obstacle, the so-called foundation.
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Francia
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina