SOLVABILITY OF THE NONLINEAR DIRICHLET PROBLEM WITH INTEGRO-DIFFERENTIAL OPERATORS

被引：3

作者：

Bayraktar, Erhan ^{[1
]}

Song, Qingshuo ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] City Univ Hong Kong, Kowloon, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 01期

基金：

美国国家科学基金会;

关键词：

boundary value problem; Skorokhod topology; integro-differential equation; viscosity solution; Levy process; stochastic exit control problem; STOCHASTIC PERRONS METHOD; VISCOSITY SOLUTIONS; LIFETIME RUIN; EQUATIONS; VERIFICATION; PROBABILITY;

D O I：

10.1137/17M1130241

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper analyzes the solvability of a class of elliptic nonlinear Dirichlet problems with jumps. The contribution of the paper is the construction of the supersolution required in Perron's method. This is achieved by solving the exit time problem of an Ito jump diffusion. The proof of this relies on the proof of continuity of the entrance time and point with respect to the Skorokhod topology.

引用

页码：292 / 315

页数：24

共 50 条

[1] The obstacle problem for nonlinear integro-differential operators
Janne Korvenpää
Tuomo Kuusi
Giampiero Palatucci
[J]. Calculus of Variations and Partial Differential Equations, 2016, 55
[2] The obstacle problem for nonlinear integro-differential operators
Korvenpaa, Janne
Kuusi, Tuomo
Palatucci, Giampiero
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (03)
[3] On the solvability of a nonlinear integro-differential equation arising in the income distribution problem
Khachatryan, A. Kh.
Khachatryan, Kh. A.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (10) : 1702 - 1711
[4] On the solvability of a nonlinear integro-differential equation arising in the income distribution problem
A. Kh. Khachatryan
Kh. A. Khachatryan
[J]. Computational Mathematics and Mathematical Physics, 2010, 50 : 1702 - 1711
[5] On solvability of boundary value problem for a nonlinear Fredholm integro-differential equation
Assanova, A. T.
Zhumatov, S. S.
Mynbayeva, S. T.
Karakenova, S. G.
[J]. BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2022, 105 (01): : 25 - 34
[6] A nonlinear parabolic integro-differential problem with an unknown Dirichlet boundary condition
Grimmonprez, Marijke
Slodicka, Marian
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 275 : 421 - 432
[7] On Solvability of Integro-Differential Equations
De Leon-Contreras, Marta
Gyongy, Istvan
Wu, Sizhou
[J]. POTENTIAL ANALYSIS, 2021, 55 (03) : 443 - 475
[8] On Solvability of Integro-Differential Equations
Marta De León-Contreras
István Gyöngy
Sizhou Wu
[J]. Potential Analysis, 2021, 55 : 443 - 475
[9] Inverse spectral problem for integro-differential operators
Kuryshova, Yu. V.
[J]. MATHEMATICAL NOTES, 2007, 81 (5-6) : 767 - 777
[10] An inverse nodal problem for integro-differential operators
Kuryshova, Yulia V.
Shieh, Chung-Tsun
[J]. JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2010, 18 (04): : 357 - 369

← 1 2 3 4 5 →