Liouville properties and critical value of fully nonlinear elliptic operators

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• 作者：Martino Bardi^a ; ^{bardi@math.unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Annalisa Cesaroni^b ; ^{annalisa.cesaroni@unipd.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B53 ; 35B40 ; 35J70 ; 35J60 ; 49L25
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 October 2016
• 年：2016
• 卷：261
• 期：7
• 页码：3775-3799
• 全文大小：404 K

文摘

We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in Ornstein–Uhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully nonlinear parabolic equations. The second is the solvability of an ergodic Hamilton–Jacobi–Bellman equation that identifies a unique critical value of the operator.