Existence for a Cauchy–Dirichlet problem for evolutional p-Laplacian systems

Abstract

Abstract. We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L 1 -function as external force. The key ingredient is the maximum principle for weak solutions.

Lq estimates of gradients for evolutional p-Laplacian systems

“…(1.4) (refer to [19]; [ First, we now estimate the difference of u from v in the local L p -norm. Let us use the notation in (2.12) for the integral average.…”