TITLE

An approximation result for solutions of Hessian equations

AUTHOR(S)
Urbas, John
PUB. DATE
June 2007
SOURCE
Calculus of Variations & Partial Differential Equations;Jun2007, Vol. 29 Issue 2, p219
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We show that W 2, p weak solutions of the k-Hessian equation F k ( D 2 u) = g( x) with k≥ 2 can be approximated by smooth k-convex solutions v j of similar equations with the right hands sides controlled uniformly in C 0,1 norm, and so that the quantities $$ \int_{B_r} (\Delta v_j)^{p-k+1} F_{k-1}(D^2v_j) $$ are bounded independently of j. This result simplifies the proof of previous interior regularity results for solutions of such equations. It also permits us to extend certain estimates for smooth solutions of degenerate two dimensional Monge–Ampère equations to W 2, p solutions.
ACCESSION #
24476008

 

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