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math.AP2023
Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems
Sunghan Kim, Kaj Nyström
We prove new optimal regularity results for obstacle problems involving evolutionary -Laplace type operators in the degenerate regime . Our main results include…
math.AP2023
Constraint maps with free boundaries: the obstacle case
Alessio Figalli, Sunghan Kim, Henrik Shahgholian
This paper revives a four-decade-old problem concerning regularity theory for (continuous) constraint maps with free boundaries. Dividing the map into two parts, the distance part…