Boundedness and Regularity with Nonlinear Dependence of Hessian and Gradient


1 Department of Mathematics,Sharif University of Technology

2 Department of Mathematical Sciences,Sharif University of Technology


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.