On a condition for the nonexistence of \(W\)-solutions of nonlinear high-order equations with L\(^1\) -data

Abstract

In a bounded open set of â„ⁿ we consider the Dirichlet problem for nonlinear 2m-order equations in divergence form with L¹ -right-hand sides. It is supposed that 2 â‰¤ m < n, and the coefficients of the equations admit the growth of rate p − 1 > 0 with respect to the derivatives of order m of unknown function. We establish that under the condition p ≤ 2 − m/n for some L¹ -data the corresponding Dirichlet problem does not have W-solutions.