EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC PDES WITH FRACTIONAL LAPLACIANS ON OPEN BALLS

被引：0

作者：

Penent, Guillaume ^{[1
]}

Privault, Nicolas ^{[1
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, 21 Nanyang Link, Singapore 637371, Singapore

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 08期

关键词：

Elliptic PDEs; semilinear PDEs; branching processes; fractional Lapla-cian; stable processes; subordination; Monte-Carlo method; BRANCHING DIFFUSION REPRESENTATION; POHOZAEV IDENTITY; DIRICHLET PROBLEM; REGULARITY; WEAK;

D O I：

10.3934/cpaa.2023081

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of viscosity solutions for fractional semilinear elliptic PDEs on open balls with bounded exterior condition in dimension d & GE; 1. Our approach relies on a tree-based probabilistic representation based on a (2s)-stable branching processes for all s & ISIN; (0, 1), and our existence results hold for sufficiently small exterior conditions and nonlinearity coefficients. In comparison with existing approaches, we consider a wide class of polynomial nonlinearities without imposing upper bounds on their maximal degree or number of terms. Numerical illustrations are provided in large dimensions.

引用

页码：2646 / 2660

页数：15

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