Holder continuity of bounded generalized solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and natural growth terms

• Main Author: Mykhailo V. Voitovych
• Format: Article
• Language: English
• Published: Texas State University 2017-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Nonlinear elliptic equations; strengthened coercivity; lower-order term; natural growth; bounded solution, Holder continuity
• Online Access: http://ejde.math.txstate.edu/Volumes/2017/63/abstr.html

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.