Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution

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.

Keywords

doubly nonlinear evolution, Hölder estimates, eigenvalue problem, fractional $p$-Laplacian, nonlocal equation

Mathematical Subject Classification 2010

Primary: 35J60, 47J35, 35J70, 35R09

Milestones

Received: 18 November 2015

Revised: 16 May 2016

Accepted: 17 June 2016

Published: 3 October 2016

Authors

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 Sweden

Vol. 9, No. 6, 2016

Ryan Hynd and Erik Lindgren

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors