On large solutions for fractional Hamilton-Jacobi equations

被引：0

作者：

Davila, Gonzalo ^{[1
]}

Quaas, Alexander ^{[1
]}

Topp, Erwin ^{[2
,3
]}

机构：

[1] Univ Tecn Federico Santa Maria, Dept Matemat, Casilla V-110,Avda Espana 1680, Valparaiso, Chile

[2] Univ Santiago Chile, Dept Matemat & CC, Casilla 307, Santiago 454003, Chile

[3] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ, Brazil

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2023年

关键词：

Dirichlet problem; Hamilton-Jacobi equations; large solutions; nonlocal operator; viscosity solutions; BLOW-UP SOLUTIONS; ELLIPTIC-EQUATIONS;

D O I：

10.1017/prm.2023.59

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence of large solutions for nonlocal Dirichlet problems posed on a bounded, smooth domain, associated with fully nonlinear elliptic equations of order 2 s, with s ? (1/2, 1), and a coercive gradient term with subcritical power 0 < p < 2 s. Due to the nonlocal nature of the diffusion, new blow-up phenomena arise within the range 0 < p < 2 s, involving a continuum family of solutions and/or solutions blowing-up to -8 on the boundary. This is in striking difference with the local case studied by Lasry-Lions for the subquadratic case 1 < p < 2.

引用

页数：23

共 50 条

[1] On the large time behavior of solutions of Hamilton-Jacobi equations
Barles, G
Souganidis, PE
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 31 (04) : 925 - 939
[2] Minimax solutions of Hamilton-Jacobi equations with fractional coinvariant derivatives*
Gomoyunov, Mikhail Igorevich
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2022, 28
[3] Minimax solutions to the Hamilton-Jacobi equations
Subbotin A.I.
[J]. Journal of Mathematical Sciences, 2001, 103 (6) : 772 - 777
[4] Hypercontractivity of solutions to Hamilton-Jacobi equations
Goldys, B
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2001, 51 (04) : 733 - 743
[5] Singularities of solutions of Hamilton-Jacobi equations
Cannarsa, Piermarco
Cheng, Wei
[J]. arXiv, 2021,
[6] On viscosity solutions of Hamilton-Jacobi equations
Zagatti, Sandro
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (01) : 41 - 59
[7] SEMICONTINUOUS SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
ROZYEV, I
SUBBOTIN, AI
[J]. PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 1988, 52 (02): : 141 - 146
[8] Stochastic Solutions to Hamilton-Jacobi Equations
Rezakhanlou, Fraydoun
[J]. Springer Proceedings in Mathematics and Statistics, 2019, 282 : 206 - 238
[9] REPRESENTATION OF SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
ISHII, H
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1988, 12 (02) : 121 - 146
[10] Hypercontractivity of Solutions to Hamilton-Jacobi Equations
Beniamin Goldys
[J]. Czechoslovak Mathematical Journal, 2001, 51 : 733 - 743

← 1 2 3 4 5 →