Mykhailo V. Voitovych
Abstract:
In this article we extend the author's previous results on the existence
of bounded generalized solutions of a Dirichlet problem for 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. Namely, we prove
the Holder continuity of bounded generalized solutions of such equations.
Submitted November 11, 2016. Published March 2, 2017.
Math Subject Classifications: 35B45, 35B65, 35J40, 35J62.
Key Words: Nonlinear elliptic equations; strengthened coercivity;
lower-order term; natural growth; bounded solution, Holder continuity.
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Mykhailo V. Voitovych Institute of Applied Mathematics and Mechanics National Academy of Sciences of Ukraine Gen. Batiouk Str. 19, 84116 Sloviansk, Ukraine email: voitovichmv76@gmail.com |
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