Optimality in nonlocal time-dependent obstacle problems
Ioannis Athanasopoulos, Luis Caffarelli, Emmanouil Milakis
TL;DR
This paper demonstrates how quasiconvexity can be used to analyze the regularity and continuity of the temporal derivative in nonlocal time-dependent obstacle problems, advancing understanding of their mathematical properties.
Contribution
It introduces a novel approach leveraging quasiconvexity to establish optimal regularity and continuity conditions for solutions in nonlocal obstacle problems.
Findings
Quasiconvexity aids in proving regularity of the temporal derivative.
Conditions for continuity of the temporal derivative are established.
The approach improves understanding of nonlocal obstacle problem solutions.
Abstract
This paper showcases the effectiveness of the quasiconvexity property in addressing the optimal regularity of the temporal derivative and establishes conditions for its continuity in nonlocal time-dependent obstacle problems.
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Taxonomy
TopicsOptimization and Variational Analysis · Nonlinear Differential Equations Analysis · Contact Mechanics and Variational Inequalities