Hölder continuity of solutions of second-order non-linear elliptic integro-differential equations

An alternative approach to find a modulus of continuity for solutions of the rescaled equation (see (6) below) for large slopes could be to apply the Harnack inequality from [15] to

In particular, we give different equivalent definitions of solutions, we state and prove a general stability result and we propose a nonlocal version of Jensen–Ishii’s lemma for

We then deduce from the Jensen’s maximum principle and the Alexandrov’s theorem (deep results in the convex analysis, see [2] and [3]), the following lemma, the last claim of which

In Section 2, we study the comparison of viscosity solutions of the Dirichlet boundary value problem (1), (8)2. In Section 3, we study the comparison of viscosity solutions of

SONER, Optimal control of jump-Markov processes and viscosity solutions, in Stochastic Differential Systems, Stochastic Control Theory and Applications,

Finally, we remark that this proof is restricted to the planar case as in the uniformly elliptic case, since the Morry type estimate of the energy is not enough to guarantee

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