Some interior regularity results for solutions of Hessian Equations

Research Report MRR98-063

Some interior regularity results for solutions of Hessian Equations

John Urbas

Abstract: We prove monotonicity formulae related to degenerate k-Hessian equations which yield Morrey type estimates for certain integrands involving the second derivatives of the solution.In the special case k=2 we deduce that weak solutions in $W^{2,p}(\O)$ , p>n-1, have locally Hölder continuous gradients. In the nondegenerate case we also show that weak solutions in $W^{2,p}(\O)$ , p>kn/2, have locally bounded second derivatives.

Download paper: PDF file (270K)

gzipped DVI file (38K)

Download cover sheet: PDF file (52K)

DVI file (2K)

Select this link for a text-only version of this abstract.

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/

Download paper:	PDF file (270K)
	gzipped DVI file (38K)

Download cover sheet:	PDF file (52K)
	DVI file (2K)