On a Condition for the Nonexistence of W-Solutions of Nonlinear High-Order Equations with L¹ -Data

  • Alexander A. Kovalevsky Institute of Applied Mathematics and Mechanics, Rosa Luxemburg St. 74, 83114 Donetsk, Ukraine.
  • Francesco Nicolosi Department of Mathematics and Informatics, University of Catania, 95125 Catania, Italy.
Keywords: Nonlinear high-order equations in divergence form, L1 -data, Dirichlet problem, W-solution, nonexistence of W-solutions

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.

Published
2012-06-01
How to Cite
[1]
A. A. Kovalevsky and F. Nicolosi, “On a Condition for the Nonexistence of W-Solutions of Nonlinear High-Order Equations with L¹ -Data”, CUBO, vol. 14, no. 2, pp. 175–182, Jun. 2012.