تقرير
A variational approach to the eigenvalue problem for complex Hessian operators
| العنوان: | A variational approach to the eigenvalue problem for complex Hessian operators |
|---|---|
| المؤلفون: | Badiane, Papa, Zeriahi, Ahmed |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematics - Analysis of PDEs, 32U05, 32W20, 35J66, 35J96 |
| الوصف: | Let $1 \leq m \leq n$ be two integers and $\Omega \Subset \C^n$ a bounded $m$-hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue and an associated eigenfunction which is $m$-subharmonic with finite energy for general twisted complex Hessian operators of order $m$. Under some extra assumption on the twist measure we prove H\"older continuity of the corresponding eigenfunction. Moreover we give applications to the solvability of more general degenerate complex Hessian equations with the right hand side depending on the unknown function. Comment: We have corrected the statement concerning the Holder continuity of the solution in the main results |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.04437 |
| رقم الأكسشن: | edsarx.2306.04437 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |