Abstract
We prove some a priori estimates as well as existence and stability theorems for the weak solutions of the complex Hessian equations in domains of and on compact Kähler manifolds. We also show optimal integrability for -subharmonic functions with compact singularities, thus partially confirming a conjecture of Błocki. Finally we obtain a local regularity result for 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.
Citation
Sławomir Dinew. Sławomir Kołodziej. "A priori estimates for complex Hessian equations." Anal. PDE 7 (1) 227 - 244, 2014. https://doi.org/10.2140/apde.2014.7.227
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