FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 99-112

On the sets of boundedness of solutions for a class of degenerate nonlinear elliptic fourth-order equations with $L1$-data

A. A. Kovalevsky
F. Nicolosi

Abstract

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In this article, we deal with a class of degenerate, nonlinear, elliptic fourth-order equations in divergence form with coefficients satisfying a strengthened ellipticity condition and right-hand sides of the class $L1$ depending on the unknown function. We consider the Dirichlet problem for equations of the given class and prove the existence of solutions of this problem bounded on the sets where the behavior of the data of the problem and the weighted functions involved is sufficiently regular.

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Last modified: February 17, 2007