A PRIORI ESTIMATES FOR COMPLEX HESSIAN EQUATIONS

作者：Dinew Slawomir^*; Kolodziej Slawomir

来源：Analysis & PDE, 2014, 7(1): 227-244.

DOI：10.2140/apde.2014.7.227

• Hessian equation
• a priori estimate
• pluripotential theory

We prove some L-infinity 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 Kahler 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,W-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.

• 出版日期2014