Interior C1 + ...-Regularity of Solutions of Two-Dimesional Variational Problems with Obstacles.
Stefan Hildebrandt (1973)
Mathematische Zeitschrift
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Displaying similar documents to “Remarks on the Regularity of Weak Solutions to Some Variational Inequalities.”
Interior C1 + ...-Regularity of Solutions of Two-Dimesional Variational Problems with Obstacles.
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We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field...
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S. Hildebrandt, H.C. Wente (1973/74)
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Banach Center Publications
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A frictional contact problem with adhesion for viscoelastic materials with long memory
Abderrezak Kasri (2021)
Applications of Mathematics
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We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...