Nonlinear parabolic equations with natural growth in general domains

We prove an existence result for a class of parabolic problems whose principal part is the p-Laplace operator or a more general Leray-Lions type operator, and featuring an additional first order term which grows like |∇u|^ p. Here the spatial domain can have infinite measure, and the data are not regular enough to ensure the boundedness of solutions. As a consequence, solutions are obtained in a class of functions with exponential integrability.