A priori estimates for the complex Hessian equations

Details A priori estimates for the complex Hessian equations A priori estimates for the complex Hessian equations

2011-12-13

arxiv.org/abs/1112.3063v1

Mathematics

Complex Variables

18 pages, preliminary version

Scientific paper

We prove some $L^{\infty}$ a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of $C^n$ and on compact K\"ahler manifolds. We also show optimal $L^p$ integrability for m-subharmonic functions with compact singularities, thus partially confirming a conjecture of Blocki. Finally we obtain a local regularity result for $W^{2,p}$ solutions of the real and complex Hessian equations under suitable regularity assumptions on the right hand side. In the real case the method of this proof improves a result of Urbas.

Affiliated with

Also associated with

No associations

Rating

A priori estimates for the complex Hessian equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A priori estimates for the complex Hessian equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A priori estimates for the complex Hessian equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-224980