Directional differentiability for the solution map of the bilateral parabolic obstacle problem
Year: 2026
Type: preprint
Abstract: We prove that the solution map of the classical bilateral parabolic obstacle problem is directionally differentiable when interpreted as a function between suitable Lebesgue and Sobolev spaces. To the best of our knowledge, this paper is the first to establish this kind of differentiability for a parabolic evolution variational inequality with two-sided fully distributed pointwise inequality constraints. Our analysis relies on known differentiability results for unilateral parabolic obstacle problems and a new theorem on the directional differentiability of solution operators of non-expansive parameterized fixed-point equations. The latter may also be of interest for other applications. Our results can be used, for example, to derive optimality conditions for optimal control problems governed by bilateral parabolic obstacle problems.
Source: arXiv (Cornell University)
Authors: Simon Blomeyer, Constantin Christof
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212366421