Hessian equations on exterior domain

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• 作者：Xu Cao ^{xcao@mail.bnu.edu.cn} ; Jiguang Bao ; ^{jgbao@bnu.edu.cn}
• 关键词：Generalized symmetric function ; Exterior Dirichlet problem ; k-Hessian equation ; Existence ; Perron's method
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：22-43
• 全文大小：416 K
• 卷排序：448

文摘

In the paper, we consider the Hessian equation σk(λ(D2u))=f(x)σk(λ(D2u))=f(x) where f   is a positive function outside a bounded domain of RnRn, n≥3n≥3 and f(x)=1+O(|x|−β)f(x)=1+O(|x|−β) for some β>2β>2 at infinity. Using the Perron's method we prove the existence and uniqueness for viscosity solutions of exterior Dirichlet problem with prescribed asymptotic behavior at infinity. There are examples to show that the result is optimal. This is an extension of the theorems given by Bao–Li–Li in [2] for f≡1f≡1 and Bao–Li–Zhang in [3] for k=nk=n.