Abstract
This article deals with a class of degenerate nonlinear elliptic fourth-order equations with L 1 -right-hand sides. Equations of the given class have divergence form and their coefficients satisfy a strengthened ellipticity condition with two different weights associated, respectively, to the first- and the second-order derivatives of unknown function. Under suitable hypotheses on the weighted functions involved we establish solvability in a Sobolev space of Dirichlet problem for equations under consideration.
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