Nonexistence of Nontrivial Weak Solutions of Some Nonlinear Inequalities with Gradient Nonlinearity
- Authors: Admasu V.E.1, Galakhov E.I.1, Salieva O.A.2
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Affiliations:
- Peoples’ Friendship University of Russia (RUDN University)
- Moscow State Technological University “Stankin”
- Issue: Vol 67, No 1 (2021): Partial Differential Equations
- Pages: 1-13
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/27888
- DOI: https://doi.org/10.22363/2413-3639-2021-67-1-1-13
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Abstract
In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient conditions for the absence of nontrivial weak solutions to nonlinear inequalities and systems with integer powers of|the Laplace operator and with a nonlinear term of the form a(x)|∇(Δmu)|q+ b(x)|∇u|s. We obtainoptimal a priori estimates by applying the nonlinear capacity method with an appropriate choice of testfunctions. As a result, we prove the absence of nontrivial weak solutions to nonlinear inequalities and systems by contradiction.
About the authors
V. E. Admasu
Peoples’ Friendship University of Russia (RUDN University)
Author for correspondence.
Email: galakhov@rambler.ru
Moscow, Russia
E. I. Galakhov
Peoples’ Friendship University of Russia (RUDN University)
Email: galakhov@rambler.ru
Moscow, Russia
O. A. Salieva
Moscow State Technological University “Stankin”
Email: olga.a.salieva@gmail.com
Moscow, Russia
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