Boundedness and Regularity with Nonlinear Dependence of Hessian and Gradient

Mehri, B.; Nojumi, M.H.

Boundedness and Regularity with Nonlinear Dependence of Hessian and Gradient

Authors

B. Mehri ¹

M.H. Nojumi ²

¹ Department of Mathematics,Sharif University of Technology

² Department of Mathematical Sciences,Sharif University of Technology

Abstract

Sucient conditions for the boundedness and regularity of a function, whose partial derivatives
satisfy a certain set of equations, are presented. Energy methods are used to establish these
results. The asymptotic behavior of the gradient toward a constant function is also investigated.

Keywords

Boundedness

Regularity

Asymptotic behavior

Nonlinear ODE

Hessian

Gradient