LAUSR

Abstract We deal with a Cauchy–Dirichlet problem with homogeneous boundary conditions on the parabolic boundary of a space–time cylinder for doubly nonlinear parabolic equations, whose prototype is ∂ t u − div ( | u | m − 1 | D u | p − 2 D u ) = f with a non-negative Lebesgue function f on the right-hand side, where p > 2 n n + 2 and m > 0 . The central objective is to establish the existence of weak solutions under the optimal integrability assumption on the inhomogeneity f. The constructed solution is obtained by a limit of approximations, i.e. we use solutions of regularized Cauchy–Dirichlet problems and pass to the limit to receive a solution for the original Cauchy–Dirichlet problem.