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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06407h.htm

Last modified: February 17, 2007