A priori estimates for complex Hessian equations

DOI10.2140/APDE.2014.7.227zbMATH Open1297.32020arXiv1112.3063OpenAlexW3103965411MaRDI QIDQ2509676

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Publication date: 29 July 2014

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Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1112.3063

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