Author:
Biswas Anup,Lőrinczi József
Abstract
Abstract
We show a strong maximum principle and an Alexandrov-Bakelman-Pucci estimate for the weak solutions of a Cauchy problem featuring Caputo time-derivatives and non-local operators in space variables given in terms of Bernstein functions of the Laplacian. To achieve this, first we propose a suitable meaning of a weak solution, show their existence and uniqueness, and establish a probabilistic representation in terms of time-changed Brownian motion. As an application, we also discuss an inverse source problem.
Subject
Applied Mathematics,Analysis
Reference68 articles.
1. Universal constraints on the location of extrema of eigenfunctions of non-local Schrödinger operators;arXiv:1711.09267,2017
2. An elementary proof of the Titchmarsh’s convolution theorem;Proc. Amer. Math. Soc.,1998
3. Asymptotic estimates of multi-dimensional stable densities and their applications;Trans. Amer. Math. Soc.,2007
4. Normal and anomalous dispersion of gravel tracer particles in rivers;J. Geophys. Res.,2010
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献