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Using a classical technique introduced by Achi E. Brandt for elliptic equations, we study a general class of nonlocal equations obtained as a superposition of classical and fractional operators in different variables. We obtain that the increments of the derivative of the solution in the direction of a variable experiencing classical diffusion are controlled linearly, with a logarithmic correction. From this, we obtain Hölder estimates for the solution.
|Journal||Nonlinear Differential Equations and Applications|
|Publication status||Published - 1 Aug 2019|
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- 1 Finished
Nonlocal Equations at Work
30/06/17 → 31/12/22