Abstract
This paper is concerned with the existence of viscosity solutions of nonlocal fully nonlinear equations that are not translation-invariant. We construct a discontinuous viscosity solution of such a nonlocal equation by Perron's method. If the equation is uniformly elliptic, we prove the discontinuous viscosity solution is Hölder continuous and thus it is a viscosity solution.
| Original language | English |
|---|---|
| Pages (from-to) | 1227-1254 |
| Journal | Analysis and PDE |
| Volume | 10 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Jul 2017 |
| Externally published | Yes |
Research Keywords
- Hamilton-jacobi-bellman-isaacs equation
- Integro-PDE
- Perron's method
- Viscosity solution
- Weak harnack inequality
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