Characterization of the coincidence set for mixed signorini problems

Abstract

For a mixed Signorini problem, reduction to a boundary variational inequality is derived. It is shown that its solution is a function constituted, on one portion of the boundary, of the upper-skirting function of solutions family of some associated linear mixed boundary value problems and, on the other portion, of the lower-skirting function of the same family. Qualitative behavior of the solution on different portions when perturbing the unknown boundary is analyzed. This shows in particular the usefulness of reduction to the boundary in some linear and nonlinear elliptic problems, even when usual variational methods cannot be applied for such purpose.

Keywords:

• Unilateral problem
• boundary variational inequality
• mixed Signorini problem
• perturbed contact zone
• coincidence set

AMS:

• 35B05
• 35C15
• 35J85
• 65R20