Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

¹ Dipartimento di Matematica e Informatica, Università della Calabria, via Pietro Bucci, cubo 31b, 87036 Rende (CS), Italy.
fabio.punzo@unical.it
² Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany ; Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy ; Istituto di Matematica Applicata e Tecnologie Informatiche “Enrico Magenes”, Consiglio Nazionale delle Ricerche, Via Ferrata 1, 27100 Pavia, Italy, and School of Mathematics and Statistics, University of Melbourne, 813 Swanston Street, Parkville VIC 3010, Australia.
enrico@math.utexas.edu

Received: 14 July 2016
Accepted: 14 December 2016

Abstract

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.