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Smooth dependence on data of solutions and contact regions for a Signorini problem. (English) Zbl 1183.35150
Summary: We prove that the solutions to a 2D Poisson equation with unilateral boundary conditions of Signorini type as well as their contact intervals depend smoothly on the data. The result is based on a certain local equivalence of the unilateral boundary value problem to a smooth abstract equation in a Hilbert space and on an application of the Implicit Function Theorem to that equation.

MSC:
35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
47J07 Abstract inverse mapping and implicit function theorems involving nonlinear operators
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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