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A
priori estimates for complex Hessian equations
Sławomir Dinew and Sławomir Kołodziej |
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Vol. 7 (2014), No. 1, 227–244
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Abstract |
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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. |
Keywords
Hessian equation, a priori estimate, pluripotential theory
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Mathematical Subject Classification 2010
Primary: 32U15
Secondary: 32U05
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Milestones
Received: 6 February 2013
Accepted: 27 November 2013
Published: 7 May 2014
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Authors |
| Sławomir Dinew | |
| Mathematics Department Rutgers Unversity Newark, NJ 07102 United States |
Department of Mathematics and
Computer Science Jagiellonian University ul. Lojasiewicza 6 30-348 Krakow Poland |
| Sławomir Kołodziej | |
| Department of Mathematics and
Computer Science Jagiellonian University ul Lojasiewicza 6 30-348 Krakow Poland |
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