This thesis involves various regularity results of nonlocal elliptic equations with Orlicz growth.
First, we prove the existence and uniqueness of a weak solution to a nonlocal Dirichlet problem with Orlicz growth by using variational methods.
Next, we show local Hölder continuity of a weak solution to such a nonlocal elliptic equation by obtaining a suitable Sobolev-Poincaré type inequality and a logarithmic estimate.
Finally, we derive Harnack inequality by finding a precise tail estimate.