Harnack inequality and self-similar solutions for fully nonlinear fractional parabolic equations

被引：0
作者：
Gonzalo Dávila
Alexander Quaas
Erwin Topp
机构：
[1] Universidad Técnica Federico Santa María,Departamento de Matemática
[2] Universidad de Santiago de Chile,Departamento de Matemática y C.C.
来源：
Calculus of Variations and Partial Differential Equations | 2023年 / 62卷
关键词：
35K55; 35D40; 35A08;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We find bounds for the principal eigenvalue and eigenfunction associated to the existence of self-similar solutions to a fully nonlinear parabolic problem. In contrast with the local case, the upper and lower bounds for the eigenfunction are of the same polynomial order |x|-(N+2s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|x|^{-(N+2s)}$$\end{document}. In order to accomplish this we prove a Harnack inequality for general nonlocal elliptic equations with zero order terms.
引用
收藏
相关论文
共 49 条
  • [1] Armstrong S(2010)Long-time asymptotics for fully nonlinear homogeneous parabolic equations Calc. Var. Partial Differ. Equ. 38 521-540
  • [2] Trokhimtchouk M(2019)A Note on the Monotonicity of Solutions for Fractional Equations in half-space Proc. AMS 213 629-650
  • [3] Barrios B(2014)A Widder’s type theorem for the Heat equation with nonlocal diffusion Arch. Ration. Mech. Anal. 357 837-850
  • [4] García-Melián J(2005)Harnack inequalities for non-local operators of variable order Trans. Am. Math. Soc. 17 375-388
  • [5] Quaas A(2002)Harnack inequalities for jump processes Potential Anal. 47 47-92
  • [6] Barrios B(1994)The principal eigenvalue and maximum principle for second order elliptic operators in general domains Commun. Pure Appl. Math. 186 469-507
  • [7] Peral I(2007)Liouville-type results for semilinear elliptic equations in unbounded domains Ann. Mat. Pura Appl. 95 263-273
  • [8] Soria F(1960)Some theorems on stable processes Trans. Am. Math. Soc. 133 53-92
  • [9] Valdinoci E(1999)Potential theory for the s-stable Schrödinger operator on bounded Lipschitz domains Studia Math. 250 242-284
  • [10] Bass RF(2014)Quantitative local and global a priori estimates for fractional nonlinear diffusion equations Adv. Math. 31 23-53
12345