On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint

被引：2
|
作者：
D'Ovidio, Mirko [1 ]
机构：
[1] Sapienza Univ Rome, Dept Basic & Appl Sci Engn, Via A Scarpa 10, I-00161 Rome, Italy
来源：
MATHEMATICS | 2022年 / 10卷 / 21期
关键词：
non-local operators; boundary value problems; initial value problems; irregular domains; time changes; FRACTIONAL CAUCHY-PROBLEMS; EQUATIONS; DERIVATIVES;
D O I：
10.3390/math10214122
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems lead to anomalous behavior on the bulk and on the surface of a given domain, respectively. Such a behavior should be considered (in a macroscopic viewpoint) in order to describe regular motion on irregular domains (in the microscopic viewpoint).
引用
收藏
页数：26
相关论文
共 50 条
  • [31] Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension
    Cunha, Gabriel Neves
    Faraci, Francesca
    Silva, Kaye
    MATHEMATICS, 2024, 12 (18)
  • [32] On the solvability of a boundary value problem on the real line
    Cupini, Giovanni
    Marcelli, Cristina
    Papalini, Francesca
    BOUNDARY VALUE PROBLEMS, 2011, : 1 - 17
  • [33] On non-local representations of the ageing algebra
    Henkel, Malte
    Stoimenov, Stoimen
    NUCLEAR PHYSICS B, 2011, 847 (03) : 612 - 627
  • [34] Fractional dynamics with non-local scaling
    Tarasov, Vasily E.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2021, 102
  • [35] Non-local relativistic δ-shell interactions
    Heriban, Lukas
    Tusek, Matej
    LETTERS IN MATHEMATICAL PHYSICS, 2024, 114 (03)
  • [36] Local Attractors in a Certain Boundary-Value Problem for the Kuramoto–Sivashinsky Equation
    Kulikov A.N.
    Sekatskaya A.V.
    Journal of Mathematical Sciences, 2020, 248 (4) : 430 - 437
  • [37] Liouville theorems for non-local operators
    Priola, E
    Zabczyk, J
    JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 216 (02) : 455 - 490
  • [38] On a Lagrangian method for the convergence from a non-local to a local Korteweg capillary fluid model
    Charve, Frederic
    Haspot, Boris
    JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (07) : 1264 - 1323
  • [39] The initial boundary value problem and quasi-local Hamiltonians in general relativity
    An, Zhongshan
    Anderson, Michael T.
    CLASSICAL AND QUANTUM GRAVITY, 2021, 38 (15)
  • [40] A matrix-free interpretation of the non-local Dirichlet-to-Neumann radiation boundary condition
    Malhotra, M
    Pinsky, PM
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1996, 39 (21) : 3705 - 3713
12345