HOLDER ESTIMATES AND LARGE TIME BEHAVIOR FOR A NONLOCAL DOUBLY NONLINEAR EVOLUTION

被引：10

作者：

Hynd, Ryan ^{[1
]}

Lindgren, Erik ^{[2
]}

机构：

[1] Univ Penn, Dept Math, Philadelphia, PA 19104 USA

[2] Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

来源：

ANALYSIS & PDE | 2016年 / 9卷 / 06期

基金：

瑞典研究理事会;

关键词：

doubly nonlinear evolution; Holder estimates; eigenvalue problem; fractional p-Laplacian; nonlocal equation; FRACTIONAL P-LAPLACIAN; PARABOLIC EQUATIONS; BOUNDED DOMAINS; ASYMPTOTIC-BEHAVIOR; DIFFUSION EQUATIONS; EIGENVALUE PROBLEMS; VISCOSITY SOLUTIONS; INEQUALITIES; CONTINUITY; GRADIENT;

D O I：

10.2140/apde.2016.9.1447

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The nonlinear and nonlocal PDE vertical bar nu(t)vertical bar(p-2) nu(t) + (-Delta p)(s)nu = 0, where (-Delta(p))(s) v(x,t) = 2 P.V. integral(Rn) vertical bar nu(x,t) - nu(x+y,t)vertical bar(p-2)nu(x,t)-nu(x,y,t))/vertical bar y vertical bar(n+sp) dy; has the interesting feature that an associated Rayleigh quotient is nonincreasing in time along solutions. We prove the existence of a weak solution of the corresponding initial value problem which is also unique as a viscosity solution. Moreover, we provide Hlder estimates for viscosity solutions and relate the asymptotic behavior of solutions to the eigenvalue problem for the fractional p-Laplacian.

引用

页码：1447 / 1482

页数：36

共 48 条

[1] Large time asymptotics of the doubly nonlinear equation in the non-displacement convexity regime [J].