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.
@article{1347,
title = {On a Condition for the Nonexistence of W-Solutions of Nonlinear High-Order Equations with L$^1$ -Data},
journal = {CUBO, A Mathematical Journal},
volume = {14},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/1347}
}
Kovalevsky, Alexander A.; Nicolosi, Francesco. On a Condition for the Nonexistence of W-Solutions of Nonlinear High-Order Equations with L¹ -Data. CUBO, A Mathematical Journal, Tome 14 (2012) . http://gdmltest.u-ga.fr/item/1347/