A variational approach to complex Hessian equations in C-n
Journal article, 2015

Let Omega be an m-hyperconvex domain of C-n and beta be the standard lathier form in C-n. We introduce finite energy classes of ni,subharmonic functions of Cegrell type, epsilon(p)(m)(Omega), p > 0 and F-m(Omega). Using a variational method we show that the degenerate complex Hessian equation (ddc phi)(m) A beta(n-m) = mu has a unique solution in epsilon(1)(m)(Omega) if and only if every function in a epsilon(1)(m) is integrable with respect to mu. If has finite total mass and does not charge m-polar sets, then the equation has a unique solution in F-m (Omega). (C) 2015 Elsevier Inc. All rights reserved.

Complex Hessian equations

Cegrell's class

Variational approach

Author

Hoang Chinh Lu

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 431 1 228-259

Subject Categories

Mathematics

DOI

10.1016/j.jmaa.2015.05.067

More information

Created

10/7/2017