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Nonlocal equations with gradient constraints

Safdari, M ; Sharif University of Technology | 2023

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  1. Type of Document: Article
  2. DOI: 10.1007/s00526-023-02536-0
  3. Publisher: Springer Science and Business Media Deutschland GmbH , 2023
  4. Abstract:
  5. We prove the existence and C1,α regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be C1 or strictly convex. We also obtain C0 , 1 boundary regularity for these problems. Our approach is to show that these nonlocal equations with gradient constraints are related to some nonlocal double obstacle problems. Then we prove the regularity of the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
  6. Keywords:
  8. Source: Calculus of Variations and Partial Differential Equations ; Volume 62, Issue 7 , 2023 ; 09442669 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00526-023-02536-0