Vol. 9, No. 6, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11
Issue 3, 555–812
Issue 2, 263–553
Issue 1, 1–261

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution

Ryan Hynd and Erik Lindgren

Vol. 9 (2016), No. 6, 1447–1482

The nonlinear and nonlocal PDE

|vt|p2v t + (Δp)sv = 0,


(Δp)sv(x,t) = 2  P.V.n|v(x,t) v(x + y,t)|p2(v(x,t) v(x + y,t)) |y|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 Hölder estimates for viscosity solutions and relate the asymptotic behavior of solutions to the eigenvalue problem for the fractional p-Laplacian.

doubly nonlinear evolution, Hölder estimates, eigenvalue problem, fractional $p$-Laplacian, nonlocal equation
Mathematical Subject Classification 2010
Primary: 35J60, 47J35, 35J70, 35R09
Received: 18 November 2015
Revised: 16 May 2016
Accepted: 17 June 2016
Published: 3 October 2016
Ryan Hynd
Department of Mathematics
University of Pennsylvania
Philadelphia, PA 19104
United States
Erik Lindgren
Department of Mathematics
Royal Institute of Technology
100 44 Stockholm