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

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DOI:

https://doi.org/10.4067/S0719-06462012000200009

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.

Keywords

Nonlinear high-order equations in divergence form , L1 -data , Dirichlet problem , W-solution , nonexistence of W-solutions
  • 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.
  • Pages: 175–182
  • Date Published: 2012-06-01
  • Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

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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 L\(^1\) -data”, CUBO, vol. 14, no. 2, pp. 175–182, Jun. 2012.

Issue

Vol. 14 No. 2 (2012): CUBO, A Mathematical Journal

Section

Articles