Choquard equation involving mixed local and nonlocal operators

In this article, we study an elliptic problem involving an operator of mixed order with both local and nonlocal aspects and in the presence of critical nonlinearity of Hartree type. To this end, we first investigate the corresponding Hardy-Littlewood-Sobolev inequality and detect the optimal constant. Using variational methods and a Pohožaev identity we then show the existence and nonexistence results for the corresponding subcritical perturbation problem.