Summability of solutions of some degenerate nonlinear elliptic fourth-order equations

Abstract

We consider a class of degenerate nonlinear elliptic fourth-order equations in divergence form. Coefficients of the equations satisfy a strengthened ellipticity condition involving two weighted functions. Existence of solutions of Dirichlet problem for equations of the given class in the case where these equations have L ¹-right-hand sides depending on unknown function has been established in our recent article. In the present article we prove some results which show the improvement of summability of solutions of the same problem under additional conditions on right-hand sides of the equations under consideration.

Keywords:

• Degenerate nonlinear elliptic fourth-order equations
• Dirichlet problem
• Summability of solutions
• AMS Mathematics Subject Classifications: 35J40
• 35J60
• 35J70

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Francesco Nicolosi ‡

E-mail: [email protected]