Dirichlet problems for fully anisotropic elliptic equations

The existence of a nontrivial bounded solution to the Dirichlet problem, for a class of nonlinear elliptic equations involving a fully anisotropic partial differential operator, is established. The relevant operator depends on the gradient of the unknown through the differential of a general convex function. This function need not be radial, nor have a polynomial type growth. Besides providing genuinely new conclusions, our result recovers and embraces, in a unified framework, several contributions in the existing literature, and augments them in various special instances.