arXiv Analytics

Sign in

arXiv:2408.07528 [math.AP]AbstractReferencesReviewsResources

Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value

Nguyen Van Phu, Nguyen Quang Dieu

Published 2024-08-14Version 1

In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-\chi(u)H_{m}(u)=\mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary value $f\in\mathcal{N}_m(\Omega)\cap MSH_m(\Omega).$

Comments: 10 pages
Categories: math.AP, math.CV
Subjects: 32U05, 32W20
Related articles: Most relevant | Search more
arXiv:math/0312508 [math.AP] (Published 2003-12-30, updated 2006-11-01)
Subharmonic functions, mean value inequality, boundary behavior, nonintegrability and exceptional sets
arXiv:math/0106078 [math.AP] (Published 2001-06-11)
Characterization of harmonic and subharmonic functions via mean-value properties
arXiv:2401.11572 [math.AP] (Published 2024-01-21)
Uniform $L^\infty$ estimates: subsolutions to fully nonlinear partial differential equations

Links

Toolbox