On a condition for the nonexistence of \(W\)-solutions of nonlinear high-order equations with L\(^1\) -data
Author
Kovalevsky, Alexander A.
Nicolosi, Francesco
Full text
https://revistas.ufro.cl/ojs/index.php/cubo/article/view/134710.4067/S0719-06462012000200009
Abstract
In a bounded open set of ℝn we consider the Dirichlet problem for nonlinear 2m-order equations in divergence form with L1 -right-hand sides. It is supposed that 2 ≤ 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.