[HTML][HTML] Obstacle problems for integro-differential operators: higher regularity of free boundaries
N Abatangelo, X Ros-Oton - Advances in Mathematics, 2020 - Elsevier
Advances in Mathematics, 2020•Elsevier
We study the higher regularity of free boundaries in obstacle problems for integro-differential
operators. Our main result establishes that, once free boundaries are C 1, α, then they are
C∞. This completes the study of regular points, initiated in [5]. In order to achieve this, we
need to establish optimal boundary regularity estimates for solutions to linear nonlocal
equations in C k, α domains. These new estimates are the core of our paper, and extend
previously known results by Grubb (for k=∞) and by the second author and Serra (for k= 1).
operators. Our main result establishes that, once free boundaries are C 1, α, then they are
C∞. This completes the study of regular points, initiated in [5]. In order to achieve this, we
need to establish optimal boundary regularity estimates for solutions to linear nonlocal
equations in C k, α domains. These new estimates are the core of our paper, and extend
previously known results by Grubb (for k=∞) and by the second author and Serra (for k= 1).
We study the higher regularity of free boundaries in obstacle problems for integro-differential operators. Our main result establishes that, once free boundaries are C 1, α, then they are C∞. This completes the study of regular points, initiated in [5]. In order to achieve this, we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in C k, α domains. These new estimates are the core of our paper, and extend previously known results by Grubb (for k=∞) and by the second author and Serra (for k= 1).
Elsevier
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