A variational approach to complex Hessian equations in C-n
Artikel i vetenskaplig tidskrift, 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

Författare

Hoang Chinh Lu

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Mathematical Analysis and Applications

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

Vol. 431 228-259

Ämneskategorier

Matematik

DOI

10.1016/j.jmaa.2015.05.067