Michail V. Voitovich
Abstract:
In this article, we consider nonlinear elliptic
fourth-order equations with the principal part satisfying a
strengthened coercivity condition, and a lower-order term having a
"natural" growth with respect to the derivatives of the unknown
function. We assume that there is an absorption term in the equation,
but we do not assume that the lower-order term satisfies
the sign condition with respect to unknown function.
We prove the existence of bounded generalized solutions for the Dirichlet
problem, and present some a priori estimates.
Submitted April 5, 2013. Published April 24, 2013.
Math Subject Classifications: 35B45, 35B65, 35J40, 35J62.
Key Words: Nonlinear elliptic equations; strengthened coercivity;
lower-order term; natural growth; Dirichlet problem;
bounded solution; L-infinity-estimate.
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Michail V. Voitovich Institute of Applied Mathematics and Mechanics Rosa Luxemburg Str. 74, 83114 Donetsk, Ukraine email: voytovich@bk.ru |
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