The present article investigates the existence, multiplicity and regularity
of weak solutions of problems involving a combination of critical Hartree type
nonlinearity along with singular and discontinuous nonlinearity. By applying
variational methods and using the notion of generalized gradients for Lipschitz
continuous functional, we obtain the existence and the multiplicity of weak
solutions for some suitable range of λ and γ. Finally by
studying the L∞-estimates and boundary behavior of weak solutions, we
prove their H\"{o}lder and Sobolev regularity