The author considers the homogeneous Dirichlet problem for linear second order uniformly elliptic equations in nondivergence form of the type \[ \sum^n_{i,j = 1} a_{ij} \partial_i \partial_ju + \sum^n_{i = 1} b_i \partial_iu + cu = f \quad \text{in} \quad \Omega, \] where \(\Omega \subset \mathbb{R}^n\) is a bounded domain with \(C^{1,1}\)-boundary, and \(f \in L^p(\Omega)\) with \(1n\) for \(p=n\) and \(t=p\) for \(p>n)\), \(c \in L^s(\Omega)\) (where \(s=n/2\) for \(1n/2\) for \(p=n/2\) and \(s=p\) for \(p>n/2)\) and \(c \leq 0\) a.e. in \(\Omega\). Existence and uniqueness of a solution \(u \in W^{2,p}(\Omega) \cap W_0^{1,p}(\Omega)\) and its continuous dependence on the right hand side \(f\) are proved.